Stats Chapter 9 and 10

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Exhibit 10-10 The results of a recent poll on the preference of shoppers regarding two products are shown below. Product Shoppers Surveyed Shoppers Favoring This Product A 800 560 B 900 612 Refer to Exhibit 10-10. The 95% confidence interval estimate for the difference between the populations favoring the products is a. -0.024 to 0.064 b. 0.6 to 0.7 c. 0.024 to 0.7 d. 0.02 to 0.3

a. -0.024 to 0.064

Exhibit 10-5 The following information was obtained from matched samples. Individual Method 1 Method 2 1 7 5 2 5 9 3 6 8 4 7 7 5 5 6 Refer to Exhibit 10-5. The point estimate for the difference between the means of the two populations (Method 1 Method 2) is a. -1 b. 0 c. -4 d. 2

a. -1

For a one-tailed test (lower tail) at 89.8% confidence, Z = a. -1.27 b. -1.53 c. -1.96 d. -1.64

a. -1.27

A two-tailed test is performed at 95% confidence. The p-value is determined to be 0.09. The null hypothesis a. must be rejected b. should not be rejected c. could be rejected, depending on the sample size d. has been designed incorrectly

b. should not be rejected

A pooled sample proportion can be computed when testing to see if 2 population proportions are equal. The pooled value represents an estimate of the unknown ___.

Population proportion

The choice of an appropriate test for comparing two population means depends on whether we deal with

Qualitative or quantitative data Independent or matched-pairs sampling The equality or lack of equality of population variances

Suppose that the competing hypotheses for a test are Ho: uD = 0 versus HA: uD (not = to) 0. If the p-value for the hypothesis test is 0.04 and the chosen level of significance is 0.05, then the correct conclusion is:

Reject Ho; the mean difference significantly differs from 0

Exhibit 10-5 The following information was obtained from matched samples. Individual Method 1 Method 2 1 7 5 2 5 9 3 6 8 4 7 7 5 5 6 Refer to Exhibit 10-5. If the null hypothesis is tested at the 5% level, the null hypothesis a. should be rejected b. should not be rejected c. should be revised d. None of these alternatives is correct.

b. should not be rejected

In hypothesis testing if the null hypothesis is rejected, a. no conclusions can be drawn from the test b. the alternative hypothesis is true c. the data must have been accumulated incorrectly d. the sample size has been too small

b. the alternative hypothesis is true

Which of the following is not a restriction for comparing two population means?

The equality of the sample sizes

Exhibit 10-12 The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below. Music Type Teenagers Surveyed Teenagers Favoring This Type Pop 800 384 Rap 900 450 Refer to Exhibit 10-12. The point estimate for the difference between the proportions is a. -0.02 b. 0.048 c. 100 d. 66

a. -0.02

The t distribution that you find your critical values closely resembles the normal distribution when:

the sample size is large

In hypothesis testing, a. the smaller the Type I error, the smaller the Type II error will be b. the smaller the Type I error, the larger the Type II error will be c. Type II error will not be effected by Type I error d. the sum of Type I and Ttype II errors must equal to 1

b. the smaller the Type I error, the larger the Type II error will be

Regarding inferences about the difference between two population means, the sampling design that uses a pooled sample variance in cases of equal population standard deviations is based on

independent samples.

Of the two production methods, a company wants to identify the method with the smaller population mean completion time. One sample of workers is selected and each worker first uses one method and then uses the other method. The sampling procedure being used to collect completion time data is based on

matched samples.

When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as

matched samples.

Generally, the ________ sample procedure for inferences about two population means provides better precision than the _______ sample approach.

matched, independent

Two or more random samples are considered independent if the process that generates 1 sample Is completely separate from the process that generate the other sample When examining the difference between 2 population means, if the populations cannot be assumed normal, then (x̅ 1- x̅ 2) is approximately normal if

n1 (> or = to) 30 and n2 (> or = to) 30

When examining the difference between 2 population means, if the populations cannot be assumed normal, then (x̅1- x̅ 2) is approximately normal if

n1 (> or = to) 30 and n2 (> or = to) 30

When developing an interval estimate for the difference between two population means with sample sizes of n1 and n2,

n1 and n2 can be of different sizes.

If the underlying populations cannot be assumed to be normal, then by the central limit theorem, the sampling distribution of is xbar1-xbar2 approximately normal only if both sample sizes are sufficiently large—that is, when

n1 ≥ 30, n2 ≥30

The sampling distribution of p̄ 1 - p̄ 2 is approximated by a normal distribution if _____ are all greater than or equal to

n1p1, n1(1 - p1), n2p2, n2(1 - p2)

The sampling distribution of p̄ 1 - p̄ 2 is approximated by a

normal distribution.

It is appropriate to conduct a hypothesis test for the difference between two population proportions under independent sampling:

only if n1pbar1 ≥ 5, n1(1-pbar1) ≥ 5, n2pbar2 ≥ 5 and n2(1-p2) ≥ 30.

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. We are interested in determining if the accident proportions differ between the two age groups. Let pu represent the proportion under and po the proportion over the age of 18. The null hypothesis is

pu - po = 0

When drawing inferences about the mean of one population, the 95% confidence interval contains all the null-hypothesized values of the population mean that should be

retained using the .05 criterion significance

The critical t value for a one-group experiment will never be

smaller than the corresponding critical z

The standard error of x̄ 1 - x̄ 2 is the

standard deviation of the sampling distribution of x̄ 1 - x̄ 2.

Which of the following does not need to be known in order to compute the p-value?

the level of significance

When drawing inferences about the mean of one population, the correct statistical model to use is

the normal curve if the population standard deviation is known and the t distributions if the population standard deviation is not known

The normal distribution can be used to test hypotheses about population proportions accurately, even with fairly small samples, if

the sample proportion is close to .5

The critical t values that are used to find a confidence interval for the population mean will get larger if:

the sample size becomes smaller

In testing the null hypothesis H0: /1 - μ2 = 0, the computed test statistic is z=-1.66. The corresponding p-value is

.0970

A researcher finds that 15 out of 45 customers in Store 1 like a particular brand of cereal and 20 out of 40 customers in Store 2 like the same brand. The sample proportions for store 1 and Store 2 are ___ and ___, respectively.

0.33 & 0.50

The 95% confidence interval for the mean of a population is 25.8 to 40.1. Which of the following cannot be the 99% confidence interval for the same population mean?

27.0 to 38.9

In the test for comparing two population means when population variances are unknown and unequal, a student calculates the degrees of freedom using the proper formula as 34.7. How many degrees of freedom should the student assume to find the p-value of the test?

A particular bank has two loan modification programs for distressed borrowers: Home Affordable Modification Program (HAMP) modifications, where the federal government pays the bank $1,000 for each successful modification, and non-HAMP modifications, where the bank does not receive a bonus from the federal government. In order to qualify for a HAMP modification, borrowers must meet a set of financial suitability criteria. What type of hypothesis test should we use to test whether borrowers from this particular bank who receive HAMP modifications are more likely to re-default than those who receive non-HAMP modifications?

A hypothesis test for p1-p2

A particular personal trainer works primarily with track and field athletes. She believes that her clients run faster after going through her program for six weeks. How might she test that claim?

A matched pairs hypothesis test for μD.

What type of test for population means should be performed when examining a situation in which employees are first tested, then trained, and finally retested?

A t test under dependent sampling

If the sampling distribution of xbar1-xbar2 cannot be assumed normal, we

Are unable to compute a confidence interval

Statistical inference concerning the mean difference based on matched-pair sampling requires 1 of 2 conditions. Select the 2 conditions.

Both X1 & X2 are normally distributed The sample size n (> or = to) 30

The 99% confidence interval for the mean of a population is 102.7 to 120.4. Which of the following cannot be 95% confidence interval for the same population mean?

Both of the above Above: 100.3 - 122.8 98.6-124.5

Independent random samples are

Completely unrelated to one another

What type of data is required to compare prices of the same textbooks sold by two different vendors?

Dependent random samples with quantitative data

Suppose that the competing hypotheses for a test are Ho: uD = 0 versus HA: uD (not =) 0. At 95% confidence interval for the mean difference is calculated as [-1.5, 4.2]. At 5% significance level, the correct conclusion to the hypothesis test is:

Do not reject Ho; the mean difference doesn't significantly differ from 0

Suppose that competing hypotheses for a test are Ho: p1 - p2 =0 versus HA: p1- p2 (not = to) 0. If the p-value is 0.045 and the significance level is 0.01, then the correct conclusion to the hypothesis test is:

Do not reject Ho; the population proportions are not significantly different

You would like to determine if there is a higher incidence of smoking among women than among men in a neighborhood. Let women and men be represented by populations 1 and 2, respectively. The relevant hypotheses are constructed as

H0: p1-p2 ≤ 0 HA: p1-p2 > 0

If the underlying populations cannot be assumed to be normal, then by the central limit theorem, the sampling distribution xbar1-xbar2 of is approximately normal only if the sum of the sample observations is sufficiently large—that is, when n1+n2 ≥ 30.

False

The confidence interval for the difference μ1-μ2 is based on the same approach used in the case of one sample: Point Estimate ± Standard Error.

False

The difference between the two sample means xbar1-xbar2 is an interval estimator of the difference between two population means μ1-μ2.

False

The necessary condition for a matched-pairs sample is that the same individual gets sampled twice

False

Two random samples are considered independent if the observations in the first sample are different from the observations of the second sample.

False

We always deal with matched-pairs sampling if two samples have the same number of observations.

False

When the population variances are unknown & cannot be assumed equal, we calculate a pooled estimate of the population variance.

False

You would like to determine if there is a higher incidence of smoking among women than among men in a neighborhood. Let men and women be represented by populations 1 and 2, respectively. The relevant hypotheses are constructed as

H0: (p1-p2) ≥ 0 HA: p1-p2 < 0

If the hypothesized difference between 2 population proportion is 0, then the standard error can be improved by computing a

Pooled estimate of the proportion

A demographer wants to measure life expectancy in countries 1 and 2. Let μ1 and μ2 denote the mean life expectancy in countries 1 and 2, respectively. Specify the hypothesis to determine if life expectancy in country 1 is more than 10 years lower than in country 2.

H0: μ1-μ2 ≥ -10 HA: μ1-μ2 < -10

Which of the following pairs of hypotheses are used to test if the mean of the first population is smaller than the mean of the second population, using independent random sampling?

H0: μ1-μ2 ≥ 0 HA: μ1-μ2 < 0

Which of the following set of hypotheses are used to test if the mean of the first population is smaller than the mean of the second population, using matched-paired sampling?

H0: μd ≥ 0 HA: μd < 0

A particular bank has two loan modification programs for distressed borrowers: Home Affordable Modification Program (HAMP) modifications, where the federal government pays the bank $1,000 for each successful modification, and non-HAMP modifications, where the bank does not receive a bonus from the federal government. In order to qualify for a HAMP modification, borrowers must meet a set of financial suitability criteria. Define the null and alternative hypotheses to test whether borrowers who receive HAMP modifications default less than borrowers who receive non-HAMP modifications. Let and represent the proportion of borrowers who received HAMP and non-HAMP modifications that did not re-default, respectively.

HO: p1-p2 ≥ 0 HA: p1-p2 < 0

When testing if 2 population proportions differ, the competing hypotheses are

Ho: p1 - p2 = 0 versus HA: p1 - p2 (not = to) 0

The competing hypotheses for a left-tailed matched-pairs test concerning the difference are constructed as

Ho: uD (> or = to) do; HA: uD < do

A researcher claims that the average customer amount spent on groceries is more in Neighborhood 1 than in Neighborhood 2. The hypotheses for this claim is:

Ho:u1 - u2 (< or = to) 0 versus HA: u1 - u2 > 0

Above: population mean: 25.7, 34.2, 38.1 The 95% confidence interval for the mean of a population is 87.5 to 113.4. Using hypothesis testing and the .05 criterion of significance, which of the following null hypothesis should be rejected?

Population mean= 115.6

What type of data should be collected when examining a situation in which two candidates running in different elections are being compared in their likelihood of winning their elections?

Independent sampling with qualitative data

Suppose you want to perform a test to compare the mean GPA of all freshmen with the mean GPA of all sophomores in a college? What type of sampling is required for this test?

Independent sampling with quantitative data

Two or more random samples are considered independent if the process that generates 1 sample

Is completely separate from the process that generate the other sample

A ___ experiment looks to find a natural pairing between 1 observation in the 1st sample & 1 observation in the 2nd sample.

Matched-pairs

A specific type of dependent sampling when the samples are paired in some way is called

Matched-pairs sampling

The equality of the sample sizes

May assume any value

For matched-pairs sampling, the parameter of interest is referred to as the

Mean difference

Statistical inference concerning the difference in population means is based on the condition that the sampling distribution of (x̅ 1 - x̅ 2) follows a(n) _____ distribution.

Normal

Suppose that the competing hypotheses for a test are Ho: uD = 0 versus HA: uD (not = to) 0. The 95% confidence interval for D is 1.0 3.5, indicating that at the 5% significance level, the mean difference is

Not significant & doesn't differ from 0

We calculate a _____ estimate of the common variance, denoted sp2, when 2 population are assumed to have the same variance.

Pooled

A researcher theorizes that students at a particular university differ in intelligence from the average IQ of 100. The researcher computes the 95% confidence interval for the mean of this population. Four possible results are shown below: Result 1: 91.6-109.4 Result 2: 99.1-116.9 Result 3: 101.2-119.0 Result 4: 112.7-130.5 Which result most strongly contradicts the researcher's theory?

Result 1

A researcher theorizes that students at a particular university differ in intelligence from the average IQ of 100. The researcher computes the 95% confidence interval for the mean of this population. Four possible results are shown below: Result 1: 91.6-109.4 Result 2: 99.1-116.9 Result 3: 101.2-119.0 Result 4: 112.7-130.5 WHich result most strongly supports the researcher's theory?

Result 4

A researcher theorizes that students at a particular university differ in intelligence from the average IQ of 100. The researcher computes the 95% confidence interval for the mean of this population. Four possible results are shown below: Result 1: 91.6-109.4 Result 2: 99.1-116.9 Result 3: 101.2-119.0 Result 4: 112.7-130.5 For which result(s) should the researcher retain the null hypothesis that the population mean is equal to 100.0?

Results 1 & 2

A researcher theorizes that students at a particular university differ in intelligence from the average IQ of 100. The researcher computes the 95% confidence interval for the mean of this population. Four possible results are shown below: Result 1: 91.6-109.4 Result 2: 99.1-116.9 Result 3: 101.2-119.0 Result 4: 112.7-130.5 For which result(s) should the researcher reject the null hypothesis that the population mean is equal to 100.0?

Results 3 & 4

The point estimate for the difference between 2 population means is represented by the difference between 2

Sample means

We calculate the ____ as a point estimate of an unknown population variance.

Sample variance

A t-test is used in place of the z-score for groups when which of the following is not known?

The population standard deviation

When testing the difference between two population means under independent sampling, we use the z distribution if

The population variances are known

Two or more random samples are considered independent if

The process that generates one sample is completely separate from the process that generates the other sample

When constructing a confidence interval for the difference between 2 population means, the margin of error equals

The standard error multiplied by za/2 or ta/2df

To create a confidence interval for the proportion in a population, you need to use your sample proportion to estimate:

The standard error of the proportion

For a statistical inference regarding xbar1-xbar2, it is imperative that the sampling distribution of μ1-μ2 is normally distributed.

True

In the case when ø21 and ø22 are unknown and can be assumed equal, we can calculate a pooled estimate of the population variance.

True

The margin of error in the confidence interval for the difference μ1-μ2 equals the standard error SE(xbar1-xbar2) multiplied by either za/2 or t a/2,df or , depending on whether or not the population variances are known.

True

We convert the estimate xbar1-xbar2 into the corresponding value of the z or t test statistic by dividing the difference between xbar1-xbar2 and the hypothesized difference d0 by the standard error of the estimator xbar1-xbar2.

True

When calculating the standard error of xbar1-xbar2, under what assumption do you pool the sample variances s12 and s22 ?

Unknown population variances that are assumed equal

Exhibit 10-9 Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test. Driver Manufacturer A Manufacturer B 1 32 28 2 27 22 3 26 27 4 26 24 5 25 24 6 29 25 7 31 28 8 25 27 Refer to Exhibit 10-9. At 90% confidence the null hypothesis a. should not be rejected b. should be rejected c. should be revised d. None of these alternatives is correct.

Wala nakabutang ang answer jusme hulaan nyo nalang

In most applications, the hypothesized difference between 2 population means is ___.

Zero

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. Final examination scores from a random sample of students enrolled today and from a random sample of students enrolled five years ago were selected. You are given the following information. Today xbar: 82 σ^2: 112.5 n: 45 Five Years Ago xbar: 88 σ^2: 54 n: 36 Refer to Exhibit 10-3. The test statistic for the difference between the two population means is _____. a. -3 b. -1.5 c. -.47 d. -.65

a. -3

Exhibit 10-5 The following information was obtained from matched samples. Individual Method 1 Method 2 1 7 5 2 5 9 3 6 8 4 7 7 5 5 6 Refer to Exhibit 10-5. The 95% confidence interval for the difference between the two population means is a. -3.776 to 1.776 b. -2.776 to 2.776 c. -1.776 to 2.776 d. 0 to 3.776

a. -3.776 to 1.776

Exhibit 10-4 The following information was obtained from independent random samples. Assume normally distributed populations with equal variances. Sample 1 Sample 2 Sample Mean 45 42 Sample Variance 85 90 Sample Size 10 12 Refer to Exhibit 10-4. The 95% confidence interval for the difference between the two population means is a. -5.372 to 11.372 b. -5 to 3 c. -4.86 to 10.86 d. -2.65 to 8.65

a. -5.372 to 11.372

Exhibit 10-3 A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those to enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five -2.08 years ago was taken. You are given the following information. Today Five Years Ago 82 88 σ2 112.5 54 n 45 36 Refer to Exhibit 10-3. The 95% confidence interval for the difference between the two population means is a. -9.92 to -2.08 b. -3.92 to 3.92 c. -13.84 to 1.84 d. -24.228 to 12.23

a. -9.92 to -2.08

Exhibit 10-8 In order to determine whether or not there is a significant difference between the hourly wages of two companies, two independent random samples were selected and the following statistics were calculated. Company A Sample size: 80 Sample mean: $6.75 Population standard deviation: $1.00 Company B Sample size: 60 Sample mean: $6.25 Population standard deviation: $0.95 Refer to Exhibit 10-8. The p-value is _____. a. .0026 b. .0084 c. .0013 d. .0042

a. .0026

In testing the null hypothesis H0: μ1 - μ2 = 0, the computed test statistic is z = -1.66. The corresponding p-value is _____. a. .0485 b. .9030 c. .9515 d. .0970

a. .0485

Exhibit 10-13 In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. Company 1 n1 = 80 x1 = $10.80 σ1= $2.00 Company 2 n2 = 60 x2 = $10.00 σ2 = $1.50 Refer to Exhibit 10-13. The point estimate of the difference between the means (Company 1 - Company 2) is _____. a. .8 b. .50 c. 20 d. -20

a. .8

Some people who bought X-Game gaming systems complained about having received defective systems. The industry standard for such systems has been ninety-eight percent non-defective systems. In a sample of 120 units sold, 6 units were defective. a. Compute the proportion of defective items in the sample. b. Compute the standard error of . c. At 95% confidence using the critical value approach, test to see if the percentage of defective systems produced by X-Game has exceeded the industry standard. d. Show that the p-value approach results in the same conclusion as that of part b.

a. 0.05 b. 0.0128 c. Test statistic Z = 2.35 > 1.645; reject Ho; the number of defects has exceeded the industry standard. d. p-value (.0094) < 0.05; reject Ho.

a. 0.0668

Exhibit 10-7 In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the following data have been gathered. Downtown Store North Mall Store Sample size 25 20 Sample mean $9 $8 Sample standard deviation $2 $1 Refer to Exhibit 10-7. A 95% interval estimate for the difference between the two population means is a. 0.078 to 1.922 b. 1.922 to 2.078 c. 1.09 to 4.078 d. 1.078 to 2.922

a. 0.078 to 1.922

Choo Choo Paper Company makes various types of paper products. One of their products is a 30 mils thick paper. In order to ensure that the thickness of the paper meets the 30 mils specification, random cuts of paper are selected and the thickness of each cut is measured. A sample of 256 cuts had a mean thickness of 30.3 mils with a standard deviation of 4 mils. a. Compute the standard error of the mean. b. At 95% confidence using the critical value approach, test to see if the mean thickness is significantly more than 30 mils. c. Show that the p-value approach results in the same conclusion as that of part b.

a. 0.25 b. Test statistics t = 1.2 < 1.645; do not reject Ho. c. p-value (.1151) is between 0.1 and 0.2; do not reject Ho.

Exhibit 10-7 In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the following data have been gathered. Downtown Store North Mall Store Sample size 25 20 Sample mean $9 $8 Sample standard deviation $2 $1 Refer to Exhibit 10-7. A point estimate for the difference between the two sample means is a. 1 b. 2 c. 3 d. 4

a. 1

For a one-tailed test (upper tail), a sample size of 26 at 90% confidence, t = a. 1.316 b. -1.316 c. -1.740 d. 1.740

a. 1.316

For a two-tailed test, a sample of 20 at 80% confidence, t = a. 1.328 b. 2.539 c. 1.325 d. 2.528

a. 1.328

Exhibit 10-6 The management of a department store is interested in estimating the difference between the mean credit purchases of to using the store's credit card versus those customers using a national major credit card. You are given the following samples were selected randomly. Store's Card Sample size: 64 Sample mean: $140 Population standard deviation: $10 Major Credit Card Sample size: 49 Sample mean: $125 Population standard deviation: $8 Refer to Exhibit 10-6. A 95% confidence interval estimate for the difference (Store's Card - Major Credit Card) between the average purchases of the customers using the two different credit cards is _____. a. 11.68 to 18.32 b. 125 to 140 c. 8 to 10 d. 49 to 64

a. 11.68 to 18.32

The sampling distribution of pbar1-pbar2 is approximated by a a. normal distribution b. t-distribution with n1 + n2 degrees of freedom c. t-distribution with n1 + n2 - 1 degrees of freedom d. t-distribution with n1 + n2 + 2 degrees of freedom

a. normal distribution

Exhibit 10-1 Salary information regarding two independent random samples of male and female employees of a large company is shown below. Male Sample size: 64 Sample mean salary (in $1000s): 44 Population variance: 128 Female Sample size: 36 Sample mean salary (in $1000s): 41 Population variance: 72 Refer to Exhibit 10-1. The point estimate of the difference between the means of the two populations (Male - Female) is _____. a. 3 b. 4 c. -4 d. -28

a. 3

Exhibit 10-10 The results of a recent poll on the preference of shoppers regarding two products are shown below. Product A Shoppers Surveyed: 800 Shoppers Favoring this Product: 560 Product B Shoppers Surveyed: 900 Shopper Favoring this Product: 612 Refer to Exhibit 10-10. The standard error of pbar1-pbar2 is _____. a. 52 b. 100 c. .044 d. .0225

a. 52

A tire manufacturer has been producing tires with an average life expectancy of 26,000 miles. Now the company is advertising that its new tires' life expectancy has increased. In order to test the legitimacy of the advertising campaign, an independent testing agency tested a sample of 6 of their tires and has provided the following data. Life Expectancy (In Thousands of Miles) 28 27 25 28 29 25 a. Determine the mean and the standard deviation. b. At 99% confidence using the critical value approach, test to determine whether or not the tire company is using legitimate advertising. Assume the population is normally distributed. c. Repeat the test using the p-value approach.

a. = 27, s = 1.67 b. Ho: < 26000 Ha: > 26000 Since t = 1.47 < 3.365, do not reject Ho and conclude that there is insufficient evidence to support the manufacturer's claim. c. p-value 0.1; do not reject Ho

The Department of Economic and Community Development (DECD) reported that in 2009 the average number of new jobs created per county was 450. The department also provided the following information regarding a sample of 5 counties in 2010. County New Jobs Created In 2010 Bradley 410 Rhea 480 Marion 407 Grundy 428 Sequatchie 400 a. Compute the sample average and the standard deviation for 2010. b. We want to determine whether there has been a significant decrease in the average number of jobs created. Provide the null and the alternative hypotheses. c. Compute the test statistic. d. Compute the p-value; and at 95% confidence, test the hypotheses. Assume the population is normally distributed.

a. = 425 and s = 32.44 (rounded) b. Ho: > 450 Ha: < 450 c. Test statistic t = -1.724 d. P-value is between 0.05 and 0.1; do not reject Ho. There is no evidence of a significant decrease.

From a population of cans of coffee marked "12 ounces," a sample of 50 cans was selected and the contents of each can were weighed. The sample revealed a mean of 11.8 ounces with a standard deviation of 0.5 ounces. a. Formulate the hypotheses to test to see if the mean of the population is at least 12 ounces. b. Compute the test statistic. c. Using the p-value approach, what is your conclusion? Let = .05.

a. H0: 12 Ha: < 12 b. t = -2.83 c. p-value (.0034) < .005; therefore, reject H0

The average gasoline price of one of the major oil companies has been $2.20 per gallon. Because of cost reduction measures, it is believed that there has been a significant reduction in the average price. In order to test this belief, we randomly selected a sample of 36 of the company's gas stations and determined that the average price for the stations in the sample was $2.14. Assume that the standard deviation of the population () is $0.12. a. State the null and the alternative hypotheses. b. Compute the test statistic. c. What is the p-value associated with the above sample results? d. At 95% confidence, test the company's claim.

a. H0: 2.20 Ha: < 2.20 b. Z = -3 c. p-value = almost zero (0.0013) d. p-value < .05; reject H0; the average price has been reduced.

Identify the null and alternative hypotheses for the following problems. a. The manager of a restaurant believes that it takes a customer less than or equal to 25 minutes to eat lunch. b. Economists have stated that the marginal propensity to consume is at least 90¢ out of every dollar. c. It has been stated that 75 out of every 100 people who go to the movies on Saturday night buy popcorn.

a. H0: 25 Ha: > 25 b. H0: p 0.9 Ha: p < 0.9 c. H0: p = 0.75 Ha: p 0.75

In the past, the average age of employees of a large corporation has been 40 years. Recently, the company has been hiring older individuals. In order to determine whether there has been an increase in the average age of all the employees, a sample of 64 employees was selected. The average age in the sample was 45 years with a standard deviation of 16 years. Let = .05. a. State the null and the alternative hypotheses. b. Compute the test statistic. c. Using the p-value approach, test to determine whether or not the mean age of all employees is significantly more than 40 years.

a. H0: 40 Ha: > 40 b. t = 2.5 c. p-value (.007518) is between .005 and .01; reject H0

Ahmadi, Inc. has been manufacturing small automobiles that have averaged 50 miles per gallon of gasoline in highway driving. The company has developed a more efficient engine for its small cars and now advertises that its new small cars average more than 50 miles per gallon in highway driving. An independent testing service road-tested 64 of the automobiles. The sample showed an average of 51.5 miles per gallon with a standard deviation of 4 miles per gallon. a. Formulate the hypotheses to determine whether or not the manufacturer's advertising campaign is legitimate. b. Compute the test statistic. c. What is the p-value associated with the sample results and what is your conclusion? Let = .05.

a. H0: 50 Ha: > 50 b. t = 3 c. p-value (.0019) is less than .005; reject H0

"D" size batteries produced by MNM Corporation have had a life expectancy of 87 hours. Because of an improved production process, it is believed that there has been an increase in the life expectancy of its "D" size batteries. A sample of 36 batteries showed an average life of 88.5 hours. Assume from past information that it is known that the standard deviation of the population is 9 hours. a. Formulate the hypotheses for this problem. b. Compute the test statistic. c. What is the p-value associated with the sample results? What is your conclusion based on the p-value? Let = .05.

a. H0: 87 Ha: > 87 b. Z = 1 c. p-value = 0.1587; therefore, do not reject H0

In order to determine the average price of hotel rooms in Atlanta, a sample of 64 hotels was selected. It was determined that the average price of the rooms in the sample was $108.50 with a standard deviation of $16. a. Formulate the hypotheses to determine whether or not the average room price is significantly different from $112. b. Compute the test statistic. c. At 95% confidence using the p-value approach, test the hypotheses. Let = 0.1.

a. H0: = 112 Ha: 112 b. t = -1.75 c. p-value is between 0.025 and 0.05; therefore, do not reject H 0

A sample of 81 account balances of a credit company showed an average balance of $1,200 with a standard deviation of $126. a. Formulate the hypotheses that can be used to determine whether the mean of all account balances is significantly different from $1,150. b. Compute the test statistic. c. Using the p-value approach, what is your conclusion? Let = .05.

a. H0: = 1150 Ha: 1150 b. t = 3.57 c. p-value (almost zero) <.005; therefore, reject H0

A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. A random sample of 49 bottles is selected, and the contents are measured. The sample yielded a mean content of 11.88 ounces with a standard deviation of 0.35 ounces. a. Formulate the hypotheses to test to determine if the machine is in perfect adjustment. b. Compute the value of the test statistic. c. Compute the p-value and give your conclusion regarding the adjustment of the machine. Let = .05.

a. H0: = 12 Ha: 12 b. t = -2.4 c. p-value is between 0.01 and 0.025; therefore, reject H0

At a local university, a sample of 49 evening students was selected in order to determine whether the average age of the evening students is significantly different from 21. The average age of the students in the sample was 23 with a standard deviation of 3.5. a. Formulate the hypotheses for this problem. b. Compute the test statistic. c. Determine the p-value and test these hypotheses. Let = .05.

a. H0: = 21 Ha: 21 b. t = 4 c. p-value is almost zero; therefore, reject H0

A lathe is set to cut bars of steel into lengths of 6 centimeters. The lathe is considered to be in perfect adjustment if the average length of the bars it cuts is 6 centimeters. A sample of 121 bars is selected randomly and measured. It is determined that the average length of the bars in the sample is 6.08 centimeters with a standard deviation of 0.44 centimeters. a. Formulate the hypotheses to determine whether or not the lathe is in perfect adjustment. b. Compute the test statistic. c. Using the p-value approach, what is your conclusion? Let = .05.

a. H0: = 6 Ha: 6 b. t = 2 c. p-value (.0456) is between 0.02 and 0.05; therefore, reject H 0

Last year, a soft drink manufacturer had 21% of the market. In order to increase their portion of the market, the manufacturer has introduced a new flavor in their soft drinks. A sample of 400 individuals participated in the taste test and 100 indicated that they like the taste. We are interested in determining if more than 21% of the population will like the new soft drink. a. Set up the null and the alternative hypotheses. b. Determine the test statistic. c. Determine the p-value. d. At 95% confidence, test to determine if more than 21% of the population will like the new soft drink.

a. H0: p 0.21 Ha: p > 0.21 b. Test statistic Z = 1.96 c. p-value = 0.025 d. p-value = 0.025 < .05; therefore, reject Ho; more than 21% like the new drink.

The Bureau of Labor Statistics reported that the average yearly income of dentists in the year 2009 was $110,000. A sample of 81 dentists, which was taken in 2010, showed an average yearly income of $120,000. Assume the standard deviation of the population of dentists in 2010 is $36,000. a. We want to test to determine if there has been a significant increase in the average yearly income of dentists. Provide the null and the alternative hypotheses. b. Compute the test statistic. c. Determine the p-value; and at 95% confidence, test the hypotheses.

a. Ho: $110,000 Ha: $110,000 b. Z = 2.5 c. p-value = 0.0062 Since the p-value = 0.0062 0.05, reject Ho. Therefore, there has been a significant increase.

A producer of various kinds of batteries has been producing "D" size batteries with a life expectancy of 87 hours. Due to an improved production process, management believes that there has been an increase in the life expectancy of their "D" size batteries. A sample of 36 batteries showed an average life of 88.5 hours. Assume from past information that it is known that the standard deviation of the population is 9 hours. a. Give the null and the alternative hypotheses. b. Compute the test statistic. c. At 99% confidence using the critical value approach, test management's belief. d. What is the p-value associated with the sample results? What is your conclusion based on the p-value?

a. Ho: < 87 Ha: > 87 b. 1.00 c. Since Z = 1 < 2.33, do not reject Ho and conclude that there is insufficient evidence to support the corporation's claim. d. p-value > 0.1587; therefore do not reject Ho

Last year, 50% of MNM, Inc. employees were female. It is believed that there has been a reduction in the percentage of females in the company. This year, in a random sample of 400 employees, 180 were female. a. Give the null and the alternative hypotheses. b. At 95% confidence using the critical value approach, determine if there has been a significant reduction in the proportion of females. c. Show that the p-value approach results in the same conclusion as that of Part b.

a. Ho: p 0.5 Ha: p 0.5 b. Test statistic Z = -2.0 < -1.645; reject Ho; the proportion of female employees is significantly less than 50%. c. p-value = 0.0228 < 0.05; reject Ho.

The p-value is a probability that measures the support (or lack of support) for the a. null hypothesis b. alternative hypothesis c. either the null or the alternative hypothesis d. sample statistic

a. null hypothesis

Exhibit 10-3 A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. Today Five Years Ago 82 88 σ2 112.5 54 n 45 36 Refer to Exhibit 10-3. What is the conclusion that can be reached about the difference in the average final examination scores between the two classes? (Use a .05 level of significance.) a. There is a statistically significant difference in the average final examination scores betweenthe two classes. b. There is no statistically significant difference in the average final examination scores betweenthe two classes. c. It is impossible to make a decision on the basis of the information given. d. There is a difference, but it is not

a. There is a statistically significant difference in the average final examination scores betweenthe two classes.

What type of error occurs if you fail to reject H0 when, in fact, it is not true? a. Type II b. Type I c. either Type I or Type II, depending on the level of significance d. either Type I or Type II, depending on whether the test is one tail or two tail

a. Type II

In order to test the following hypotheses at an level of significance H0: 800 Ha: > 800 the null hypothesis will be rejected if the test statistic Z is a. Z b. < Z c. < -Z d. =

a. Z

The error of rejecting a true null hypothesis is a. a Type I error b. a Type II error c. is the same as d. committed when not enough information is available

a. a Type I error

A Type II error is committed when a. a true alternative hypothesis is mistakenly rejected b. a true null hypothesis is mistakenly rejected c. the sample size has been too small d. not enough information has been available

a. a true alternative hypothesis is mistakenly rejected

For a lower tail test, the p-value is the probability of obtaining a value for the test statistic a. at least as small as that provided by the sample b. at least as large as that provided by the sample c. at least as small as that provided by the population d. at least as large as that provided by the population.

a. at least as small as that provided by the sample

As the test statistic becomes larger, the p-value a. gets smaller b. becomes larger c. stays the same, since the sample size has not been changed d. becomes negative

a. gets smaller

An assumption made about the value of a population parameter is called a a. hypothesis b. conclusion c. confidence d. significance

a. hypothesis

To compute an interval estimate for the difference between the means of two populations, the t distribution _____. a. is not restricted to small sample situations b. none of the answers is correct c. can be applied when the populations have equal means d. is restricted to small sample situations

a. is not restricted to small sample situations

Exhibit 10-11 An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. Under Age of 18 Over Age of 18 n1 = 500 n2 = 600 Number of accidents = 180 Number of accidents = 150 We are interested in determining if the accident proportions differ between the two age groups. Refer to Exhibit 10-11. The p-value is a. less than 0.001 b. more than 0.10 c. 0.0228 d. 0.3

a. less than 0.001

The sampling distribution of pbar1 - pbar2 is approximated by a _______ a. normal distribution b. t distribution with n1+n2 degrees of freedom c. t distribution with n1+n2+2 degrees of freedom d. t distribution with n1+n2-1 degrees of freedom

a. normal distribution

Exhibit 10-11 An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. Under Age 18 n1 = 500 Number of accidents = 180 Over Age 18 n2 = 600 Number of accidents = 150 We are interested in determining if the accident proportions differ between the two age groups. Refer to Exhibit 10-11 and let pu represent the proportion under and po the proportion over the age of 18. The null hypothesis is a. pu-po=o b. pu-po>(wline)0 c. pu-po<(wline)0 d. pu - po (does not) = 0

a. pu-po=o

Exhibit 10-8 In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. Company A Company B Sample size 80 60 Sample mean $16.75 $16.25 Population standard deviation $1.00 $0.95 The null hypothesis should a. should be rejected be rejected b. should not be rejected c. should be revised d. None of these alternatives is correct.

a. should be rejected be rejected

Exhibit 10-5 The following information was obtained from matched samples. Individual Method 1 Method 2 175 259 368 477 556 Refer to Exhibit 10-5. If the null hypothesis is tested at the 5% level, the null hypothesis _____. a. should not be rejected b. should be rejected c. none of the answers is correct d. should be revised

a. should not be rejected

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes with a standard deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. Refer to Exhibit 9-4. At 95% confidence, it can be concluded that the mean of the population is a. significantly greater than 3 b. not significantly greater than 3 c. significantly less than 3 d. significantly greater then 3.18

a. significantly greater than 3

the standard error of xbar1-xbar2 is the _____ a. standard deviation of the sampling distribution of xbar1-xbar2 b. variance of xbar1-xbar2 c. difference between the two means d. variance of the sampling distribution of xbar1-xbar2

a. standard deviation of the sampling distribution of xbar1-xbar2

In the hypothesis testing procedure, is a. the level of significance b. the critical value c. the confidence level d. 1 - level of significance

a. the level of significance

There are two common methods for measuring the concentration of a pollutant in fish tissue. Do the two methods differ on the average? You apply both methods to a random sample of 18 carp and use... a. the paired t test for mean difference b. the one-sample z test for p. c. the two-sample z test for p1-p2 d. none of these. e. the two-sample t test for u1-u2

a. the paired t test for mean difference

If a hypothesis is not rejected at the 5% level of significance, it a. will also not be rejected at the 1% level b. will always be rejected at the 1% level c. will sometimes be rejected at the 1% level d. None of these alternatives is correct.

a. will also not be rejected at the 1% level

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. Under Age 18 n1 = 500 Number of accidents = 180 Over Age 18 n2 = 600 Number of accidents = 150 We are interested in determining if the accident proportions differ between the two age groups. Refer to Exhibit 10-11. The value of the test statistic is _____. a.3.96 b. 1.96 c. 2.96 d. .96

a.3.96

If we are interested in testing whether the proportion of items in population 1 is larger than the proportion of items in population 2, the

alternative hypothesis should state p1 - p2 > 0.

If we are interested in testing whether the mean of items in population 1 is larger than the mean of items in population 2, the

alternative hypothesis should state μ1 - μ2 > 0

If we specify a range of values within which a parameter (such as a population mean) is likely to fall, this range can be referred to as:

an interval estimate

When the hypothesized difference of the population proportions is equal to 0, we

are able to estimate the standard error of p1-p2, using the pooled pbar can use the confidence interval to implement the test if the difference of the population proportions is equal to 0.

Exhibit 10-12 The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below. Music Type: Pop Teenagers Surveyed: 800 Teenagers Favoring This Type: 384 Music Type: Rap Teenagers Surveyed: 900 Teenagers Favoring: 450 Refer to Exhibit 10-12. The point estimate for the difference between the proportions is _____. a. 66 b. -.02 c. .048 d. 100

b. -.02

In a lower one-tail hypothesis test situation, the p-value is determined to be 0.2. If the sample size for this test is 51, the t statistic has a value of a. 0.849 b. -0.849 c. 1.299 d. -1.299

b. -0.849

For a one-tailed test (lower tail) at 93.7% confidence, Z = a. -1.86 b. -1.53 c. -1.96 d. -1.645

b. -1.53

b. 1.80

Exhibit 10-3 A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. Final examination scores from a random sample of students enrolled today and from a random sample of students enrolled five years ago were selected. You are given the following information. Today xbar: 82 σ^2: 112.5 n: 45 Five Years Ago xbar: 88 σ^2: 54 n: 36 Refer to Exhibit 10-3. The 95% confidence interval for the difference between the two population means is _____. a. -13.84 to 1.84 b. -9.92 to -2.08 c. -24.228 to 12.23 d. -3.92 to 3.92

b. -9.92 to -2.08

b. .0026

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes with a standard deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. Refer to Exhibit 9-4. The p-value is between a. .005 to .01 b. .01 to .025 c. .025 to .05 d. .05 to .10

b. .01 to .025

Exhibit 10-10 The results of a recent poll on the preference of shoppers regarding two products are shown below. Product A Shoppers Surveyed: 800 Shoppers Favoring this Product: 560 Product B Shoppers Surveyed: 900 Shopper Favoring this Product: 612 Refer to Exhibit 10-10. The point estimate for the difference between the two population proportions in favor of this product (Product A - Product B) is _____. a. .44 b. .02 c. 100 d. 52

b. .02

Exhibit 10-2 The following information was obtained from matched samples. The daily production rates for a random sample of workers before and after a training program are shown below. Worker Before After 1 20 22 2 25 23 3 27 27 4 23 20 5 22 25 6 20 19 7 17 18 Refer to Exhibit 10-2. The null hypothesis to be tested is H0: μd = 0. The value of the test statistic is _____. a. -1.96 b. 0 c. 1.96 d. 1.645

b. 0

Exhibit 10-8 In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. Company A Company B Sample size 80 60 Sample mean $16.75 $16.25 Population standard deviation $1.00 $0.95 Refer to Exhibit 10-8. The p-value is a. 0.0013 b. 0.0026 c. 0.0042 d. 0.0084

b. 0.0026

Exhibit 9-8 The average gasoline price of one of the major oil companies in Europe has been $1.25 per liter. Recently, the company has undertaken several efficiency measures in order to reduce prices. Management is interested in determining whether their efficiency measures have actually reduced prices. A random sample of 49 of their gas stations is selected and the average price is determined to be $1.20 per liter. Furthermore, assume that the standard deviation of the population ( ) is $0.14. Refer to Exhibit 9-8. The p-value for this problem is a. 0.4938 b. 0.0062 c. 0.0124 d. 0.05

b. 0.0062

Exhibit 10-13 In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. Company 1 Company 2 n1 = 80 n2 = 60 x1= $10.80 x2 = $10.00 std dev = $2.00 std dev = $1.50 Refer to Exhibit 10-13. The p-value is a. 0.0035 b. 0.007 c. 0.4965 d. 1.96

b. 0.007

n a one-tailed hypothesis test (lower tail) the test statistic is determined to be -2. The p-value for this test is a. 0.4772 b. 0.0228 c. 0.0056 d. 0.5228

b. 0.0228

Exhibit 10-10 The results of a recent poll on the preference of shoppers regarding two products are shown below. Product Shoppers Surveyed Shoppers Favoring This Product A 800 560 B 900 612 Refer to Exhibit 10-10. At 95% confidence, the margin of error is a. 0.064 b. 0.044 c. 0.0225 d. 52

b. 0.044

Exhibit 10-11 An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. Under Age of 18 Over Age of 18 n1 = 500 n2 = 600 Number of accidents = 180 Number of accidents = 150 We are interested in determining if the accident proportions differ between the two age groups. Refer to Exhibit 10-11. The pooled proportion is a. 0.305 b. 0.300 c. 0.027 d. 0.450

b. 0.300

Exhibit 10-8 In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. Company A Company B Sample size 80 60 Sample mean $16.75 $16.25 Population standard deviation $1.00 $0.95 Refer to Exhibit 10-8. A point estimate for the difference between the two sample means is a. 20 b. 0.50 c. 0.25 d. 1.00

b. 0.50

Exhibit 10-13 In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. Company 1 Company 2 n1 = 80 n2 = 60 x1= $10.80 x2 = $10.00 std dev = $2.00 std dev = $1.50 Refer to Exhibit 10-13. The point estimate of the difference between the means is a. 20 b. 0.8 c. 0.50 d. -20

b. 0.8

Exhibit 10-7 In order to estimate the difference between the average hourly wages of employees of two branches of a department store, two independent random samples were selected and the following statistics were calculated. Downtown Store Sample size: 25 Sample mean: $9 Sample standard deviation: $2 North Mall Store Sample size: 20 Sample mean: $8 Sample standard deviation: $1 Refer to Exhibit 10-7. A point estimate for the difference between the two sample means (Downtown Store - North Mall Store) is _____. a. 3 b. 1 c. 4 d. 2

b. 1

For a two-tailed test at 86.12% confidence, Z = a. 1.96 b. 1.48 c. 1.09 d. 0.86

b. 1.48

Exhibit 10-1 Salary information regarding male and female employees of a large company is shown below. Male Female Sample Size 64 36 Sample Mean Salary (in $1,000) 44 41 Population Variance (σ2) 128 72 Refer to Exhibit 10-1. If you are interested in testing whether or not the average salary of males is significantly greater than that of females, the test statistic is a. 2.0 b. 1.5 c. 1.96 d. 1.645

b. 1.5

Exhibit 10-6 The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information. Store's Card Major Credit Card Sample size 64 49 Sample mean $140 $125 Population standard deviation $10 $8 Refer to Exhibit 10-6. A 95% confidence interval estimate for the difference between the average purchases of the customers using the two different credit cards is a. 49 to 64 b. 11.68 to 18.32 c. 125 to 140 d. 8 to 10

b. 11.68 to 18.32

Exhibit 10-6 The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information. Assume the samples were selected randomly. Store's Card Sample size: 64 Sample mean: $140 Population standard deviation: $10 Major Credit Card Sample size: 49 Sample mean: $125 Population standard deviation: $8 Refer to Exhibit 10-6. A point estimate for the difference between the mean purchases of the users of the two credit cards (Store's Card - Major Credit Card) is _____. a. 265 b. 15 c. 18 d. 2

b. 15

Exhibit 10-3 A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. Final examination scores from a random sample of students enrolled today and from a random sample of students enrolled five years ago were selected. You are given the following information. Today xbar: 82 σ^2: 112.5 n: 45 Five Years Ago xbar: 88 σ^2: 54 n: 36 Refer to Exhibit 10-3. The standard error of xbar1-xbar2 is _____ a. 4 b. 2 c. 12.9 d. 9.3

b. 2

Exhibit 10-9 Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test. Driver Manufacturer A Manufacturer B 1 32 28 2 27 22 3 26 27 4 26 24 5 25 37 6 29 37 7 31 28 8 25 Refer to Exhibit 10-9. The mean of the differences (Manufacturer A - Manufacturer B) is _____. a. 1.5 b. 2.0 c. .50 d. 2.5

b. 2.0

Exhibit 9-6 A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal. Refer to Exhibit 9-6. The test statistic is a. 1.96 b. 2.00 c. 1.645 d. 0.05

b. 2.00

Exhibit 10-1 Salary information regarding male and female employees of a large company is shown below. Male Female Sample Size 64 36 Sample Mean Salary (in $1,000) 44 41 Population Variance (σ2) 128 72 Refer to Exhibit 10-1. The point estimate of the difference between the means of the two populations is a. -28 b. 3 c. 4 d. -4

b. 3

Exhibit 10-6 The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information. Store's Card Major Credit Card Sample size 64 49 Sample mean $140 $125 Population standard deviation $10 $8 Refer to Exhibit 10-6. At 95% confidence, the margin of error is a. 1.694 b. 3.32 c. 1.96 d. 15

b. 3.32

Exhibit 10-4 The following information was obtained from independent random samples. Assume normally distributed populations with equal variances. Sample 1 Sample 2 Sample Mean 45 42 Sample Variance 85 90 Sample Size 10 12 Refer to Exhibit 10-4. The standard error of xbar1-xbar2 is a. 3.0 b. 4.0 c. 8.372 d. 19.48

b. 4.0

A study of rad rage asked separate random samples of 596 men and 523 women about their behavior while driving. Based on their answers, each respondent was assigned a road rage score on a scale of 0 to 20. Are the conditions for performing a two-sample t test satisfied? a. Maybe; we have independent random samples, but we need to look at the data to check Normality. b. Yes; we have two independent random samples and large sample sizes. c. No; we don't know the population standard deviations. d. Yes; the large sample sizes guarantee that the corresponding population distributions will be Normal. e. No; road rage scores in a range between 0 and 20 can't be Normal.

b. Yes; we have two independent random samples and large sample sizes.

To compute an interval estimate for the difference between the means of two populations, the t distribution a. is restricted to small sample situations b. is not restricted to small sample situations c. can be applied when the populations have equal means d. None of these alternatives is correct.

b. is not restricted to small sample situations

Exhibit 9-5 A random sample of 100 people was taken. Eighty-five of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 80%. Refer to Exhibit 9-5. At 95% confidence, it can be concluded that the proportion of the population in favor of candidate A a. is significantly greater than 80% b. is not significantly greater than 80% c. is significantly greater than 85% d. is not significantly greater than 85%

b. is not significantly greater than 80%

Exhibit 9-7 A random sample of 16 statistics examinations from a large population was taken. The average score in the sample was 78.6 with a variance of 64. We are interested in determining whether the average grade of the population is significantly more than 75. Assume the distribution of the population of grades is normal. Refer to Exhibit 9-7. At 95% confidence, it can be concluded that the average grade of the population a. is not significantly greater than 75 b. is significantly greater than 75 c. is not significantly greater than 78.6 d. is significantly greater than 78.6

b. is significantly greater than 75

A company wants to identify which of two production methods has the smaller completion time. One sample of workers is matched randomly selected and each worker first uses one method and then uses the other method. The sampling procedure being used to collect completion time data is based on _____ samples. a. pooled b. matched c. cross d. independent

b. matched

5. When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as a. corresponding samples b. matched samples c. independent samples d. None of these alternatives is correct.

b. matched samples

When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as _____. a. none of the answers is correct b. matched samples c. independent samples d. corresponding samples

b. matched samples

The level of significance is the a. maximum allowable probability of Type II error b. maximum allowable probability of Type I error c. same as the confidence coefficient d. same as the p-value

b. maximum allowable probability of Type I error

When developing an interval estimate for the difference between two sample means, with sample sizes of n1 and n2, _____. a. n1 must be larger than n2 b. n1 and n2 can be of different sizes c. n1 must be equal to n2 d. n1 must be smaller than n2

b. n1 and n2 can be of different sizes

Exhibit 10-2 The following information was obtained from matched samples. The daily production rates for a sample of workers before and after a training program are shown below. Worker Before After 1 20 22 2 25 23 3 27 27 4 23 20 5 22 25 6 20 19 7 17 18 Refer to Exhibit 10-2. Based on the results of question 18, the a. null hypothesis should be rejected b. null hypothesis should not be rejected c. alternative hypothesis should be accepted d. None of these alternatives is correct.

b. null hypothesis should not be rejected

How much more effective is exercise and drug treatment than drug treatment alone at reducing the rate of heart attacks among men aged 65 and older? To find out, researchers perform a completely randomized experiment involving 1000 healthy males in this age group. Half of the subjects are assigned to receive drug treatment only, while the other half area assigned to exercise regularly and to receive drug treatment. The most appropriate inference method for answering the original research question is... a. two-sample t interval for μ1 - b. two-sample z interval for p1 - p2. c. two-sample z test for p1 - p2. d. one-sample z test for proportion. e. two-sample t test for μ1 - μ2.

b. two-sample z interval for p1 - p2.

For a two-tail test, the p-value is the probability of obtaining a value for the test statistic as a. likely as that provided by the sample b. unlikely as that provided by the sample c. likely as that provided by the population d. unlikely as that provided by the population

b. unlikely as that provided by the sample

If a hypothesis is rejected at 95% confidence, it a. will always be accepted at 90% confidence b. will always be rejected at 90% confidence c. will sometimes be rejected at 90% confidence d. None of these alternatives is correct.

b. will always be rejected at 90% confidence

4. To construct an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown and it can be assumed the two populations have equal variances, we must use a t distribution with (let n1 be the size of sample 1 and n2 the size of sample 2) a. (n1 + n2) degrees of freedom b. (n1 + n2 - 1) degrees of freedom c. (n1 + n2 - 2) degrees of freedom d. n1 - n2 + 2

c. (n1 + n2 - 2) degrees of freedom

To construct an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown and it can be assumed the two populations have equal variances, we must use a t distribution with (let n1 be the size of sample 1 and n2 the size of sample 2) a. (n1+n2) degrees of freedom b. (n1+n2-1) degrees of freedom c. (n1+n2-2) degrees of freedom d. (n1-n2+2) degrees of freedom

c. (n1+n2-2) degrees of freedom

For a lower bounds one-tailed test, the test statistic z is determined to be zero. The p-value for this test is a. zero b. -0.5 c. +0.5 d. 1.00

c. +0.5

The results of a recent poll on the preference of shoppers regarding two products are shown below. Product A Shoppers Surveyed: 800 Shoppers Favoring this Product: 560 Product B Shoppers Surveyed: 900 Shopper Favoring this Product: 612 Refer to Exhibit 10-10. The 95% confidence interval estimate for the difference between the populations favoring the products is _____. a. .6 to .7 b. .024 to .7 c. -.024 to .064 d. .02 to .3

c. -.024 to .064

Exhibit 10-5 The following information was obtained from matched samples. Individual Method 1 Method 2 1 7 5 2 5 9 3 6 8 4 7 7 5 5 6 Refer to Exhibit 10-5. The null hypothesis tested is H0: μd = 0. The test statistic for the difference between the two population means is a. 2 b. 0 c. -1 d. -2

c. -1

For a one-tailed test (lower tail), a sample size of 10 at 90% confidence, t = a. 1.383 b. 2.821 c. -1.383 d. -2.821

c. -1.383

For a one-tailed test (lower tail) with 22 degrees of freedom at 95% confidence, the value of t = a. -1.383 b. 1.383 c. -1.717 d. -1.721

c. -1.717

Exhibit 9-8 The average gasoline price of one of the major oil companies in Europe has been $1.25 per liter. Recently, the company has undertaken several efficiency measures in order to reduce prices. Management is interested in determining whether their efficiency measures have actually reduced prices. A random sample of 49 of their gas stations is selected and the average price is determined to be $1.20 per liter. Furthermore, assume that the standard deviation of the population ( ) is $0.14. Refer to Exhibit 9-8. The value of the test statistic for this hypothesis test is a. 1.96 b. 1.645 c. -2.5 d. -1.645

c. -2.5

Exhibit 10-5 The following information was obtained from matched samples. Individual Method 1 Method 2 1 7 5 2 5 9 3 6 8 4 7 7 5 5 6 Refer to Exhibit 10-5. The 95% confidence interval for the mean of the population of differences is _____. a. -1.776 to 2.776 b. 0 to 3.776 c. -3.776 to 1.776 d. -2.776 to 2.776

c. -3.776 to 1.776

c. .025 to .05

Exhibit 9-7 A random sample of 16 statistics examinations from a large population was taken. The average score in the sample was 78.6 with a variance of 64. We are interested in determining whether the average grade of the population is significantly more than 75. Assume the distribution of the population of grades is normal. Refer to Exhibit 9-7. The p-value is between a. .005 to .01 b. .01 to .025 c. .025 to .05 d. .05 to 0.1

c. .025 to .05

c. .300

Exhibit 10-8 In order to determine whether or not there is a significant difference between the hourly wages of two companies, two independent random samples were selected and the following statistics were calculated. Company A Sample size: 80 Sample mean: $6.75 Population standard deviation: $1.00 Company B Sample size: 60 Sample mean: $6.25 Population standard deviation: $0.95 Refer to Exhibit 10-8. A point estimate for the difference between the two sample means (Company A Company B) is _____ a. 1.00 b. .25 c. .50 d. 20

c. .50

Exhibit 10-2 The following information was obtained from matched samples. The daily production rates for a sample of workers before and after a training program are shown below. Worker Before After 1 20 22 2 25 23 3 27 27 4 23 20 5 22 25 6 20 19 7 17 18 Refer to Exhibit 10-2. The point estimate for the difference between the means of the two populations is a. -1 b. -2 c. 0 d. 1

c. 0

Exhibit 10-2 The following information was obtained from matched samples. The daily production rates for a sample of workers before and after a training program are shown below. Worker Before After 1 20 22 2 25 23 3 27 27 4 23 20 5 22 25 6 20 19 7 17 18 Refer to Exhibit 10-2. The null hypothesis to be tested is H0: μd = 0. The test statistic is a. -1.96 b. 1.96 c. 0 d. 1.645

c. 0

Exhibit 10-10 The results of a recent poll on the preference of shoppers regarding two products are shown below. Product Shoppers Surveyed Shoppers Favoring This Product A 800 560 B 900 612 Refer to Exhibit 10-10. The standard error of pbar1-pbar2 is a. 52 b. 0.044 c. 0.0225 d. 100

c. 0.0225

c. 1.25

Exhibit 10-9 Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test. Driver Manufacturer A Manufacturer B 1 32 28 2 27 22 3 26 27 4 26 24 5 25 24 6 29 25 7 31 28 8 25 27 Refer to Exhibit 10-9. The mean for the differences is a. 0.50 b. 1.5 c. 2.0 d. 2.5

c. 2.0

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes with a standard deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. Refer to Exhibit 9-4. The test statistic is a. 1.96 b. 1.64 c. 2.00 d. 0.056

c. 2.00

For a two-tailed test at 98.4% confidence, Z = a. 1.96 b. 1.14 c. 2.41 d. 0.8612

c. 2.41

Exhibit 10-4 The following information was obtained from independent random samples. Assume normally distributed populations with equal variances. Sample 1 Sample 2 Sample Mean 45 42 Sample Variance 85 90 Sample Size 10 12 Refer to Exhibit 10-4. The degrees of freedom for the t-distribution are a. 22 b. 21 c. 20 d. 19

c. 20

Exhibit 10-4 The following information was obtained from independent random samples. Assume normally distributed populations with equal variances. Sample 1 Sample 2 Sample Mean 45 42 Sample Variance 85 90 Sample Size 10 12 Refer to Exhibit 10-4. The point estimate for the difference between the means of the two populations is a. 0 b. 2 c. 3 d. 15

c. 3

Exhibit 10-1 Salary information regarding male and female employees of a large company is shown below. Male Female Sample Size 64 36 Sample Mean Salary (in $1,000) 44 41 Population Variance (σ2) 128 72 Refer to Exhibit 10-1. At 95% confidence, the margin of error is a. 1.96 b. 1.645 c. 3.920 d. 2.000

c. 3.920

The school's newspaper reported that the proportion of students majoring in business is at least 30%. You plan on taking a sample to test the newspaper's claim. The correct set of hypotheses is a. H0: P < 0.30 Ha: P 0.30 b. H0: P 0.30 Ha: P > 0.30 c. H0: P 0.30 Ha: P < 0.30 d. H0: P > 0.30 Ha: P 0.30

c. H0: P 0.30 Ha: P < 0.30

The academic planner of a university thinks that at least 35% of the entire student body attends summer school. The correct set of hypotheses to test his belief is a. H0: P > 0.35 Ha: P 0.35 b. H0: P 0.35 Ha: P > 0.35 c. H0: P 0.35 Ha: P < 0.35 d. H0: P > 0.35 Ha: P 0.35

c. H0: P 0.35 Ha: P < 0.35

A quiz question gives random samples of n = 10 observations from each of two Normally distributed populations. John uses a table of t distribution critical values and 9 degrees of freedom to calculate a 95% confidence interval for difference in the two population means. Emily uses her calculator's two-sample t interval with 16.87 degrees of freedom to compute the 95% confidence interval. Assume that both students calculate the intervals correctly. Which of the following is true? a. Emily's confidence interval is wider. b. There is insufficient information to determine which confidence interval is wider. c. John's confidence interval is wider. d. Both confidence intervals are the same. e. Emily made a mistake; degrees of freedom has to be a whole number.

c. John's confidence interval is wider.

In a two-tailed hypothesis test situation, the test statistic is determined to be t = -2.692. The sample size has been 45. The p-value for this test is a. -0.005 b. +0.005 c. -0.01 d. +0.01

d. +0.01

If we are interested in testing whether the proportion of items in population 1 is larger than the proportion of hypothesis items in the a. null hypothesis should state P1 - P2 < 0 b. null hypothesis should state P1 - P2 ≥ 0 c. alternative hypothesis should state P1 - P2 > 0 d. alternative hypothesis should state P1 - P2 < 0

c. alternative hypothesis should state P1 - P2 > 0

we are interested in testing whether the proportion of items in population 1 is larger than the proportion of items in population 2, the a. null hypothesis should state p1 - p2 < 0 b. null hypothesis should state p1 - p2 > 0 c. alternative hypothesis should state p1 - p2 > 0 d. alternative hypothesis should state p1 - p2 < 0

c. alternative hypothesis should state p1 - p2 > 0

8. If two independent large samples are taken from two populations, the sampling distribution of the difference between the two sample means a. can be approximated by a Poisson distribution b. will have a variance of one c. can be approximated by a normal distribution d. will have a mean of one

c. can be approximated by a normal distribution

One major reason that the two-sample t procedures are widely used is that they are quite robust. This means that... a. confidence levels and P-values from the t procedures are quite accurate even if outliers and strong skewness are present. b. t procedures do not require that we know the standard deviations of the populations. c. confidence levels and P-values from the t procedures are quite accurate even if the population distribution is not exactly normal. d. t procedures compare population means, a comparison that answers many practical questions. e. t procedures work even when the random, normal, and independent conditions are violated.

c. confidence levels and P-values from the t procedures are quite accurate even if the population distribution is not exactly normal.

The level of significance a. can be any positive value b. can be any value c. is (1 - confidence level) d. can be any value between -1.96 to 1.96

c. is (1 - confidence level)

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. Under Age 18 n1 = 500 Number of accidents = 180 Over Age 18 n2 = 600 Number of accidents = 150 We are interested in determining if the accident proportions differ between the two age groups. Refer to Exhibit 10-11. The p-value is _____. a. more than .10 b. .3 c. less than .001 d. .0228

c. less than .001

The level of significance in hypothesis testing is the probability of a. accepting a true null hypothesis b. accepting a false null hypothesis c. rejecting a true null hypothesis d. None of these alternatives is correct.

c. rejecting a true null hypothesis

9. The standard error of xbar1- xbar2 is the of xbar1- a. variance of xbar1-xbar2 b. variance of the sampling distribution of xbar1-xbar2 c. standard deviation of the sampling distribution of xbar1-xbar2 d. difference between the two means

c. standard deviation of the sampling distribution of xbar1-xbar2

Independent simple random samples are selected to test the difference between the means of two populations whose variances are not known. The sample sizes are n1 = 32 and n2 = 40. The correct distribution to use is the _____ distribution. a. uniform b. normal c. t d. binomial

c. t

Which of the following does not need to be known in order to compute the p-value? a. knowledge of whether the test is one-tailed or two-tailed b. the value of the test statistic c. the level of significance d. None of these alternatives is correct.

c. the level of significance

Exhibit 10-13 In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. Company 1 n1 = 80 x1 = $10.80 σ1= $2.00 Company 2 n2 = 60 x2 = $10.00 σ2 = $1.50 Refer to Exhibit 10-13. The null hypothesis for this test is _____. a. u1-u2 does not = 0 b. u1-u2 > (w line) 0 c. u1-u2 = 0 d. u1-u2 < (w line) 0

c. u1-u2 = 0

If the level of significance of a hypothesis test is raised from .01 to .05, the probability of a Type II error a. will also increase from .01 to .05 b. will not change c. will decrease d. will increase

c. will decrease

The p-value ranges between a. zero and infinity b. minus infinity to plus infinity c. zero to one d. -1 to +1

c. zero to one

If two independent large samples are taken from two populations, the sampling distribution of the difference between the two sample means

can be approximated by a normal distribution.

Exhibit 10-12 The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below. Music Type: Pop Teenagers Surveyed: 800 Teenagers Favoring This Type: 384 Music Type: Rap Teenagers Surveyed: 900 Teenagers Favoring: 450 Refer to Exhibit 10-12. The 95% confidence interval for the difference between the two proportions is _____. a. .48 to .5 b. .028 to .068 c. 384 to 450 d. -.068 to .028

d. -.068 to .028

Exhibit 10-1 Salary information regarding two independent random samples of male and female employees of a large company is shown below. Male Sample size: 64 Sample mean salary (in $1000s): 44 Population variance: 128 Female Sample size: 36 Sample mean salary (in $1000s): 41 Population variance: 72 Refer to Exhibit 10-1. The 95% confidence interval for the difference between the means of the two populations is _____. a. -1.96 to 1.96 b. 0 to 6.92 c. -2 to 2 d. -.92 to 6.92

d. -.92 to 6.92

Exhibit 10-12 The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below. Music Type Teenagers Surveyed Teenagers Favoring This Type Pop 800 384 Rap 900 450 Refer to Exhibit 10-12. The 95% confidence interval for the difference between the two proportions is a. 384 to 450 b. 0.48 to 0.5 c. 0.028 to 0.068 d. -0.068 to 0.028

d. -0.068 to 0.028

Exhibit 10-1 Salary information regarding male and female employees of a large company is shown below. Male Female Sample Size 64 36 Sample Mean Salary (in $1,000) 44 41 Population Variance (σ2) 128 72 Refer to Exhibit 10-1. The 95% confidence interval for the difference between the means of the two populations is a. 0 to 6.92 b. -2 to 2 c. -1.96 to 1.96 d. -0.92 to 6.92

d. -0.92 to 6.92

d. -3

d. -6

d. .007

Exhibit 10-1 Salary information regarding two independent random samples of male and female employees of a large company is shown below. Male Sample size: 64 Sample mean salary (in $1000s): 44 Population variance: 128 Female Sample size: 36 Sample mean salary (in $1000s): 41 Population variance: 72 Refer to Exhibit 10-1. The p-value is _____. a. 1.96 b. 1.336 c. .0334 d. .0668

d. .0668

In a two-tailed hypothesis test the test statistic is determined to be Z = -2.5. The p-value for this test is a. -1.25 b. 0.4938 c. 0.0062 d. 0.0124

d. 0.0124

Exhibit 10-10 The results of a recent poll on the preference of shoppers regarding two products are shown below. Product Shoppers Surveyed Shoppers Favoring This Product A 800 560 B 900 612 Refer to Exhibit 10-10. The point estimate for the difference between the two population proportions in favor of this product is a. 52 b. 100 c. 0.44 d. 0.02

d. 0.02

Exhibit 9-8 The average gasoline price of one of the major oil companies in Europe has been $1.25 per liter. Recently, the company has undertaken several efficiency measures in order to reduce prices. Management is interested in determining whether their efficiency measures have actually reduced prices. A random sample of 49 of their gas stations is selected and the average price is determined to be $1.20 per liter. Furthermore, assume that the standard deviation of the population ( ) is $0.14. Refer to Exhibit 9-8. The standard error has a value of a. 0.14 b. 7 c. 2.5 d. 0.02

d. 0.02

Exhibit 10-12 The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below. Music Type Teenagers Surveyed Teenagers Favoring This Type Pop 800 384 Rap 900 450 Refer to Exhibit 10-12. The standard error of is a. 0.48 b. 0.50 c. 0.03 d. 0.0243

d. 0.0243

d. 0.1056

Read the Z statistic from the normal distribution table and circle the correct answer. A one-tailed test (upper tail) at 87.7% confidence; Z = a. 1.54 b. 1.96 c. 1.645 d. 1.16

d. 1.16

For a one-tailed test (upper tail) at 93.7% confidence, Z = a. 1.50 b. 1.96 c. 1.645 d. 1.53

d. 1.53

For a one-tailed test (upper tail), a sample size of 18 at 95% confidence, t = a. 2.12 b. -2.12 c. -1.740 d. 1.740

d. 1.740

Exhibit 10-6 The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information. Store's Card Major Credit Card Sample size 64 49 Sample mean $140 $125 Population standard deviation $10 $8 Refer to Exhibit 10-6. A point estimate for the difference between the mean purchases of the users of the two credit cards is a. 2 b. 18 c. 265 d. 15

d. 15

d. 2

Exhibit 10-1 Salary information regarding male and female employees of a large company is shown below. Male Female Sample Size 64 36 Sample Mean Salary (in $1,000) 44 41 Population Variance (σ2) 128 72 Refer to Exhibit 10-1. The standard error for the difference between the two means is a. 4 b. 7.46 c. 4.24 d. 2.0

d. 2.0

Exhibit 10-9 Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test. Driver Manufacturer A Manufacturer B 1 32 28 2 27 22 3 26 27 4 26 24 5 25 24 6 29 25 7 31 28 8 25 27 Refer to Exhibit 10-9. The test statistic is a. 1.645 b. 1.96 c. 2.096 d. 2.256

d. 2.256

Exhibit 10-13 In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. Company 1 Company 2 n1 = 80 n2 = 60 x1= $10.80 x2 = $10.00 std dev = $2.00 std dev = $1.50 Refer to Exhibit 10-13. The test statistic has a value of a. 1.96 b. 1.645 c. 0.80 d. 2.7

d. 2.7

Exhibit 10-13 In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. Company 1 n1 = 80 x1 = $10.80 σ1= $2.00 Company 2 n2 = 60 x2 = $10.00 σ2 = $1.50 Refer to Exhibit 10-13. The test statistic has a value of ______. a. .80 b. 1.645 c. 1.96 d. 2.7

d. 2.7

Exhibit 10-8 In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. Company A Company B Sample size 80 60 Sample mean $16.75 $16.25 Population standard deviation $1.00 $0.95 Refer to Exhibit 10-8. The test statistic is a. 0.098 b. 1.645 c. 2.75 d. 3.01

d. 3.01

Exhibit 10-8 In order to determine whether or not there is a significant difference between the hourly wages of two companies, two independent random samples were selected and the following statistics were calculated. Company A Sample size: 80 Sample mean: $6.75 Population standard deviation: $1.00 Company B Sample size: 60 Sample mean: $6.25 Population standard deviation: $0.95 Refer to Exhibit 10-8. The value of the test statistic is _____. a. 2.75 b. 1.645 c. .098 d. 3.01

d. 3.01

d. 3.96

In the past, 75% of the tourists who visited Chattanooga went to see Rock City. The management of Rock City recently undertook an extensive promotional campaign. They are interested in determining whether the promotional campaign actually increased the proportion of tourists visiting Rock City. The correct set of hypotheses is a. H0: P > 0.75 Ha: P 0.75 b. H0: P < 0.75 Ha: P 0.75 c. H0: P 0.75 Ha: P < 0.75 d. H0: P 0.75 Ha: P > 0.75

d. H0: P 0.75 Ha: P > 0.75

If the probability of a Type I error () is 0.05, then the probability of a Type II error () must be a. 0.05 b. 0.95 c. 0.025 d. None of these alternatives is correct.

d. None of these alternatives is correct.

Salary information regarding male and female employees of a large company is shown below. Male Female Sample Size 64 36 Sample Mean Salary (in $1,000) 44 41 Population Variance (σ2) 128 72 Refer to Exhibit 10-1. At 95% confidence, the conclusion is the a. average salary of males is significantly greater than females b. average salary of males is significantly lower than females c. salaries of males and females are equal d. None of these alternatives is correct.

d. None of these alternatives is correct.

The sum of the values of and a. always add up to 1.0 b. always add up to 0.5 c. is the probability of Type II error d. None of these alternatives is correct.

d. None of these alternatives is correct.

If the alternative hypothesis is that proportion of items in population 1 is larger than the proportion of items in population 2, then the null hypothesis should be _____. a. p1-p2 < 0 b. p1-p2 = 0 c. p1-p2 > 0 d. p1-p2 ≤ 0

d. p1-p2 ≤ 0

If a hypothesis test leads to the rejection of the null hypothesis, a. a Type II error must have been committed b. a Type II error may have been committed c. a Type I error must have been committed d. a Type I error may have been committed

d. a Type I error may have been committed

If two independent large samples are selected from two populations, the smiling distribution of the difference between the two sample means _______ a. can be approximated by a Poisson distribution b. will have a mean of 1 c. will have a variance of 1 d. can be approximated by a normal distribution

d. can be approximated by a normal distribution

The power curve provides the probability of a. correctly accepting the null hypothesis b. incorrectly accepting the null hypothesis c. correctly rejecting the alternative hypothesis d. correctly rejecting the null hypothesis

d. correctly rejecting the null hypothesis

The p-value a. is the same as the Z statistic b. measures the number of standard deviations from the mean c. is a distance d. is a probability

d. is a probability

For a one-tailed hypothesis test (upper tail) the p-value is computed to be 0.034. If the test is being conducted at 95% confidence, the null hypothesis a. could be rejected or not rejected depending on the sample size b. could be rejected or not rejected depending on the value of the mean of the sample c. is not rejected d. is rejected

d. is rejected

If a hypothesis is rejected at the 5% level of significance, it a. will always be rejected at the 1% level b. will always be accepted at the 1% level c. will never be tested at the 1% level d. may be rejected or not rejected at the 1% level

d. may be rejected or not rejected at the 1% level

3. When developing an interval estimate for the difference between two sample means, with sample sizes of n1 and n2, a. n1 must be equal to n2 b. n1 must be smaller than n2 c. n1 must be larger than n2 d. n1 and n2 can be of different sizes,

d. n1 and n2 can be of different sizes,

Exhibit 10-2 The following information was obtained from matched samples. The daily production rates for a random sample of workers before and after a training program are shown below. Worker Before After 1 20 22 2 25 23 3 27 27 4 23 20 5 22 25 6 20 19 7 17 18 Refer to Exhibit 10-2. Based on the results of the previous question, the _____. a. alternative hypothesis should be accepted b. null hypothesis should be rejected c. none of the answers is correct d. null hypothesis should not be rejected

d. null hypothesis should not be rejected

Exhibit 10-11 An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. Under Age of 18 Over Age of 18 n1 = 500 n2 = 600 Number of accidents = 180 Number of accidents = 150 We are interested in determining if the accident proportions differ between the two age groups. Refer to Exhibit 10-11 and let pu represent the proportion under and po the proportion over the age of 18. The null hypothesis is a. pu-po≤0 b. pu-po≥0 c. pu-po≠0 d. pu-po=0

d. pu-po=0

Exhibit 9-6 A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal. Refer to Exhibit 9-6. At 95% confidence, it can be concluded that the mean age is a. not significantly different from 24 b. significantly different from 24 c. significantly less than 24 d. significantly more than 24

d. significantly more than 24

7. Independent simple random samples are taken to test the difference between the means of two populations whose standard deviations are not known, but are assumed to be equal. The sample sizes are n1 = 25 and n2 = 35. The correct distribution to use is the a. t distribution with 61 degrees of freedom b. t distribution with 60 degrees of freedom c. t distribution with 59 degrees of freedom d. t distribution with 58 degrees of freedom

d. t distribution with 58 degrees of freedom

Independent simple random samples are taken to test the difference between the means of two populations whose standard deviations are not known, but are assumed to be equal. The sample sizes are n1 = 25 and n2 = 35. The correct distribution to use is the a. t distribution with 61 degrees of freedom b. t distribution with 60 degrees of freedom c. t distribution with 59 degrees of freedom d. t distribution with 58 degrees of freedom

d. t distribution with 58 degrees of freedom

6. Independent simple random samples are taken to test the difference between the means of two populations whose variances are not known, but are assumed to be equal. The sample sizes are n1 = 32 and n2 = 40. The correct distribution to use is the a. t distribution with 73 degrees of freedom b. t distribution with 72 degrees of freedom c. t distribution with 71 degrees of freedom d. t distribution with 70 degrees of freedom

d. t distribution with 70 degrees of freedom

Independent simple random samples are taken to test the difference between the means of two populations whose variances are not known, but are assumed to be equal. The sample sizes are n1 = 32 and n2 = 40. The correct distribution to use is the a. t distribution with 73 degrees of freedom b. t distribution with 72 degrees of freedom c. t distribution with 71 degrees of freedom d. t distribution with 70 degrees of freedom

d. t distribution with 70 degrees of freedom

The probability of committing a Type I error when the null hypothesis is true is a. the confidence level b. c. greater than 1 d. the Level of Significance

d. the Level of Significance

In hypothesis testing if the null hypothesis has been rejected when the alternative hypothesis has been true, a. a Type I error has been committed b. a Type II error has been committed c. either a Type I or Type II error has been committed d. the correct decision has been made

d. the correct decision has been made

Independent simple random samples are selected to test the difference between the means of two populations whose standard deviations are not known. We are unwilling to assume that the population variances are equal. The sample sizes are n1 = 25 and n2 = 35. The correct distribution to use is the t distribution with ______ degrees of freedom. a. 25 b. 35 c. 58 d. the correct degrees of freedom cannot be calculated without being given the sample standard deviations

d. the correct degrees of freedom cannot be calculated without being given the sample standard deviations

Researchers are interested in evaluating the effect of a natural product on reducing blood pressure. This will be done by comparing the mean reduction in blood pressure of a treatment (natural product) group and a placebo group using a two-sample t test. The researchers would like to be able to detect whether the natural product reduces blood pressure by at least 7 points more, on averge, than the placebo. If groups of size 50 are used in the experiment, a two-sample t test using α = 0.01 will have a power of 80% to detect a 7-point difference in mean blood pressure reduction. If the researchers want to be able to detect a 5-point difference instead, then the power of the test... a. could be either less than or greater than 80%, depending on whether the natural product is effective. b. would vary depending on the standard deviation of the data. c. would be greater than 80%. d. would be less than 80%. e. would still be 80%

d. would be less than 80%.

Exhibit 10-13 In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. Company 1 Company 2 n1 = 80 n2 = 60 x1= $10.80 x2 = $10.00 std dev = $2.00 std dev = $1.50 Refer to Exhibit 10-13. The null hypothesis for this test is a. μ1 - μ2 ≠ 0 b. μ1 - μ2 >= 0 c. μ1 - μ2 <= 0 d. μ1 - μ2 = 0

d. μ1 - μ2 = 0

If we switch from the 95% confidence interval to the 99% confidence interval:

we can be more sure that the population mean falls within the confidence interval

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