Chapter 9&10 STAT

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 Refer to Exhibit 10-2. The point estimate for the mean of the population of difference is -2 -1 1 0

0

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. Refer to Exhibit 10-2. The null hypothesis to be tested is H0: μd = 0. The value of the test statistic is 1.645 -1.96 0 1.96

0

When using Excel to calculate a p-value for an upper-tail hypothesis test, which of the following must be used?

1 − NORM.S.DIST

For a sample size of 30, changing from using the standard normal distribution to using the t distribution in a hypothesis test

will result in the rejection region being smaller

The probability of making a Type I error is denoted by 1 − α β α 1 − β

α

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.Refer to Exhibit 10-13. The null hypothesis for this test is μ1 - μ2 < 0 μ1 - μ2 ≠ 0 μ1 - μ2 = 0 μ1 - μ2 > 0

μ1 - μ2 = 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 95% confidence interval estimate for the difference between the populations favoring the products is .02 to .3 .024 to .7 -.024 to .064 .6 to .7

-.024 to .064

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 -.068 to .028 .028 to .068 384 to 450 .48 to .5

-.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 Female Sample size 64 36 Sample mean salary (in $1000s) 44 41 Population variance 128 72 Refer to Exhibit 10-1. The 95% confidence interval for the difference between the means of the two populations is -2 to 2 0 to 6.92 -1.96 to 1.96 -.92 to 6.92

-.92 to 6.92

Exhibit 10-5 The following information was obtained from matched samples. Refer to Exhibit 10-5. The null hypothesis tested is H0: μd = 0. The test statistic for the mean of the population of differences is 2 0 -2 -1

-1

Read the t statistic from the table of t distributions and circle the correct answer. A one-tailed test (lower tail), a sample size of 10 at a .10 level of significance; t =

-1.383

Read the t statistic from the table of t distributions and circle the correct answer. A one-tailed test (lower tail), a sample size of 10 at a .10 level of significance; t = _____.

-1.383

Read the z statistics from the normal distribution table and circle the correct answer. A two-tailed test at a .0694 level of significance; z = _____.

-1.48 and 1.48

Read the z statistic from the normal distribution table and circle the correct answer. A one-tailed test (lower tail) at a .063 level of significance; z = _____.

-1.53

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 Five Years Ago 82 88 σ2 112.5 54 n 45 36 Refer to Exhibit 10-3. The test statistic for the difference between the two population means is

-3

Exhibit 10-5 The following information was obtained from matched samples. Individual Method 1 Method 2 175259368477 5,5,6 Refer to Exhibit 10-5. The 95% confidence interval for the mean of the population of differences is -3.776 to 1.776 -2.776 to 2.776 0 to 3.776 -1.776 to 2.776

-3.776 to 1.776

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 Five Years Ago 82 88 σ2 112.5 54 n 45 36 Refer to Exhibit 10-3. The point estimate for the difference between the means of the two populations is 58.5 -9 9 -6

-6

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. Refer to Exhibit 10-8. The p-value is .0042 .0084 .0026 .0013

.0026

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.Refer to Exhibit 10-3. The p-value for the difference between the two population means is .0013 .4986 .9972 .0036

.0036

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 (Product A - Product B) is 100 .44 52 .02

.02

Exhibit 9-2 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. The population standard deviation is known to be 0.5 minute. 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 9-2. The p-value is

.0228

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 .48 .50 .0243 .03

.0243

For a two-tailed hypothesis test with a test statistic value of z = 2.05, the p-value is _____.

.0404

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 .0225 .064 .044 52

.044

Exhibit 10-1 Salary information regarding two independent random samples of male and female employees of a large company is shown below. Refer to Exhibit 10-1. The p-value is 1.336 .0334 .0668 1.96

.0668

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

.0970

Exhibit 9-6 A random sample of 100 people was taken. Eighty 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 75%. Refer to Exhibit 9-6. The p-value is .025 .05 .2112 .1251

.1251

Exhibit 9-3 n = 49 H0: μ = 50 = 54.8 Ha: μ ≠ 50 σ = 28 Refer to Exhibit 9-3. The p-value is equal to _____.

.2302

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 Over Age 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 .450 .027 .305 .300

.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 Company B Sample size 80 60 Sample mean $6.75 $6.25 Population standard deviation $1.00 $0.95 Refer to Exhibit 10-8. A point estimate for the difference between the two sample means (Company A - Company B) is

.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 1 = $10.80 2 = $10.00 σ1= $2.00 σ2= $1.50 Refer to Exhibit 10-13. The point estimate of the difference between the means (Company 1 - Company 2) is

.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. Refer to Exhibit 10-7. A point estimate for the difference between the two sample means (Downtown Store - North Mall Store) is 1 3 4 2

1

Read the z statistic from the normal distribution table and circle the correct answer. A one-tailed test (upper tail) at a .123 level of significance; z = _____.

1.16

Exhibit 9-3 n = 49 H0: μ = 50 = 54.8 Ha: μ ≠ 50 σ = 28 Refer to Exhibit 9-3. The test statistic equals -1.2 .3849 1.2 .1714

1.2

Exhibit 9-6 A random sample of 100 people was taken. Eighty 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 75%. Refer to Exhibit 9-6. The test statistic is

1.25

Read the t statistic from the table of t distributions and circle the correct answer. A two-tailed test, a sample of 20 at a .20 level of significance; t = 2.528 1.325 1.328 2.539

1.328

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. sample mean1: $140 sample mean2: $125 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 265 2 18 15

15

Exhibit 10-1 Salary information regarding two independent random samples of male and female employees of a large company is shown below. Sample size 64 36 Sample mean salary (in $1000s) 44 41 Population variance 128 72 Refer to Exhibit 10-1. The standard error for the difference between the two means is 7.46 2.0 4.24 4

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. Refer to Exhibit 10-9. The mean of the differences (Manufacturer A - Manufacturer B) is .50 1.5 2.5 2.0

2.0

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 19 21 20 22

20

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

3

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 3 15 2 0

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. Assume the samples were selected randomly. 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 1.694 1.96 3.32 15

3.32

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 Over Age 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 value of the test statistic is .96 2.96 3.96 1.96

3.96

Exhibit 10-4 The following information was obtained from independent random samples. Assume normally distributed populations with equal variances. Refer to Exhibit 10-4. The standard error of x1-x2 is8.372 19.48 3.0 4.0

4.0

When the hypotheses H0: μ ≥ 100 and Ha: μ < 100 are being tested at a level of significance of α, the null hypothesis will be rejected if the test statistic z is < -zα <100 > -zα > zα

< -za

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 H0: p < .75 Ha: p ≥ .75 H0: p ≤ .75 Ha: p > .75 H0: p > .75 Ha: p ≤ .75 H0: p ≥ .75 Ha: p < .75

H0: p ≤ .75 Ha: p > .75

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 H0: p < .30 Ha: p ≥ .30 H0: p ≥ .30 Ha: p < .30 H0: p ≤ .30 Ha: p > .30 H0: p > .30 Ha: p ≤ .30

H0: p ≥ .30 Ha: p < .30

Which of the following hypotheses is not a valid null hypothesis? H0: μ ≥ 0 H0: μ < 0 H0: μ ≤ 0 H0: μ = 0

H0: μ < 0

A meteorologist stated that the average temperature during July in Chattanooga was 80 degrees. A sample of July temperatures over a 32-year period was taken. The correct set of hypotheses is H0: μ < 80 Ha: μ ≤ 80 H0: μ ≠ 80 Ha: μ = 80 H0: μ ≤ 80 Ha: μ > 80 H0: μ = 80 Ha: μ ≠ 80

H0: μ = 80 Ha: μ ≠ 80

The average life expectancy of tires produced by Whitney Tire Company has been 40,000 miles. Management believes that due to a new production process, the life expectancy of its tires has increased. In order to test the validity of this belief, the correct set of hypotheses is _____.

H0: μ ≤ 40,000 Ha: μ > 40,000

Your investment executive claims that the average yearly rate of return on the stocks she recommends is at least 10.0%. You plan on taking a sample to test her claim. The correct set of hypotheses is _____.

H0: μ ≥ 10.0% Ha: μ < 10.0%

A student believes that the average grade on the final examination in statistics is at least 85. She plans on taking a sample to test her belief. The correct set of hypotheses is H0: μ > 85 Ha: μ ≤ 85 H0: μ ≤ 85 Ha: μ > 85 H0: μ ≥ 85 Ha: μ < 85 H0: μ < 85 Ha: μ ≥ 85

H0: μ ≥ 85 Ha: μ < 85

Which of the following is an improper form of the null and alternative hypotheses?

H0:m<m0 and Ha:m>=m0

Which of the following is an improper form of the null and alternative hypotheses?

Ho: u <u0 and Ha:bar under U > U0

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 Ho: p<=.35 Ha: p>.35 Ho: p>=.35 Ha: p<.35 Ho:p>.35 Ha:p>=.35 Ho:p>.35 Ha:p<=.35

Ho:p>=.35 Ha:p<.35

Excel's __________ function can be used to calculate a p-value for a hypothesis test

NORM.S.DIST

When using Excel to calculate a p-value for a lower-tail hypothesis test, which of the following must be used?

NORM.S.DIST

Which Excel function would NOT be appropriate to use when conducting a hypothesis test for a population proportion?

STDEV

Excel's __________ function can be used to calculate a p-value for a hypothesis test when σ is unknown.

T.DIST

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

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

In hypothesis testing, the hypothesis tentatively assumed to be true is _____.

The 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. 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. Refer to Exhibit 10-3. What conclusion can be reached about the difference in the average final examination scores between the two classes? (Use a .05 level of significance.)

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

If a hypothesis test leads to the rejection of the null hypothesis, a

Type I error may have been committed

The level of significance is symbolized by p σ ß a

a

The level of significance is symbolized by _____.

a

The error of rejecting a true null hypothesis is _____

a Type I error

In hypothesis testing, the critical value is _____.

a number that establishes the boundary of the rejection region

A Type II error is committed when _____.

a true alternative hypothesis is mistakenly rejected

A Type I error is committed when

a true null hypothesis is rejected

If a hypothesis is not rejected at a 5% level of significance, it will

also not be rejected at the 1% level

As a general guideline, the research hypothesis should be stated as the _____.

alternative hypothesis

Exhibit 9-1 n = 36 H0: μ ≤ 20 = 24.6 Ha: μ > 20 σ = 12 Refer to Exhibit 9-1. If the test is done at a .05 level of significance, the null hypothesis should

be rejected

For a two-tailed test with a sample size of 40, the null hypothesis will NOT be rejected at a 5% level of significance if the test statistic is

between -1.96 and 1.96, exclusively

For a two-tailed hypothesis test about a population mean, the null hypothesis can be rejected if the confidence interval

does not include µ0

For a one-tailed test (upper tail) with a sample size of 900, the null hypothesis will be rejected at the .05 level of significance if the test statistic is greater than or equal to 1.645 less than 1.645 1.645 greater than 1.645

greater than or equal to 1.645

The smaller the p-value, the _____.

greater the evidence against H0

The practice of concluding "do not reject H0" is preferred over "accept H0" when we _____

have not controlled for the Type II error

An example of statistical inference is

hypothesis testing

In tests about a population proportion, p0 represents the _____.

hypothesized population proportion

A two-tailed test is a hypothesis test in which the rejection region is

in both tails of the sampling distribution

A one-tailed test is a hypothesis test in which rejection region is

in one tail of the sampling distribution

The rejection region for a one-tailed hypothesis test _____.

is in the tail that supports the alternative hypothesis

The rejection region for a one-tailed hypothesis test is

is in the tail that supports the alternative hypothesis

To compute an interval estimate for the difference between the means of two populations, the t distribution

is not restricted to small sample situations

In a two-tailed hypothesis test, the null hypothesis should be rejected if the p-value is _____

less than or equal to a

When the rejection region is in the lower tail of the sampling distribution, the p-value is the area under the curve

less than or equal to the test statistic

If the cost of a Type I error is high, a smaller value should be chosen for the

level of significance

For a two-tailed hypothesis test about μ, we can use any of the following approaches EXCEPT compare the _____ to the _____.

level of significance; confidence coefficient

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

matched samples

The level of significance is the _____

maximum allowable probability of a Type I error

If a hypothesis is rejected at a 5% level of significance, it

may be rejected or not rejected at the 1% level

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

n-1 and n-2 can be of different sizes

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

n1 + n2 - 2

Exhibit 10-1 Salary information regarding two independent random samples of male and female employees of a large company is shown below. Male Female Sample size 64 36 Sample mean salary (in $1000s) 44 41 Population variance 128 72 Refer to Exhibit 10-1. At 95% confidence, we have enough evidence to conclude that

none of the answers is correct

Exhibit 9-3 n = 49 H0: μ = 50 = 54.8 Ha: μ ≠ 50 σ = 28 Refer to Exhibit 9-3. If the test is done at a 5% level of significance, the null hypothesis should _____.

not be rejected

Exhibit 9-4 A random sample of 16 students selected from the student body of a large university had an average age of 25 years. We want to determine if the average age of all the students at the university is significantly different from 24. Assume the distribution of the population of ages is normal with a standard deviation of 2 years. Refer to Exhibit 9-4. At a .05 level of significance, it can be concluded that the mean age is

not significantly different from 24

Exhibit 9-6 A random sample of 100 people was taken. Eighty 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 75%. Refer to Exhibit 9-6. At a .05 level of significance, it can be concluded that the proportion of the population in favor of candidate A is

not significantly greater than 75%

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 Refer to Exhibit 10-2. Based on the results of the previous question, the

null hypothesis should not be rejected

Two approaches to drawing a conclusion in a hypothesis test are

p-value and critical value

When the p-value is used for hypothesis testing, the null hypothesis is rejected if p-value ≤ α p-value = z α < p-value p-value > α

p-value ≤ a

When the p-value is used for hypothesis testing, the null hypothesis is rejected if

p-value ≤ α

A p-value is the _____

probability, when the null hypothesis is true, of obtaining a sample result that is at least as unlikely as what is observed

A two-tailed test is performed at a 5% level of significance. The p-value is determined to be .09. The null hypothesis

should not be rejected

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

should not be rejected

Exhibit 9-2 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. The population standard deviation is known to be 0.5 minute. 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 9-2. At a .05 level of significance, it can be concluded that the mean of the population is

significantly greater than 3

More evidence against H0 is indicated by

smaller p-values

In hypothesis testing if the null hypothesis is rejected, _

the evidence supports the alternative hypothesis

In hypothesis testing, the alternative hypothesis is _____.

the hypothesis concluded to be true if the null hypothesis is rejected

In the hypothesis testing procedure, α is _____.

the level of significance

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

the level of significance

If a hypothesis test has a Type I error probability of .05, that means if the null hypothesis is _____.

true, it will be rejected 5% of the time

In order to test the hypotheses H0: μ ≤ 100 and Ha: μ > 100 at an α level of significance, the null hypothesis will be rejected if the test statistic z is

≥ za