qmb 3200 exam 3 ch14, ST 560 Module 11, Chapter 13 Quiz, Chapter 8: Interval Estimation, Stat chapter 10, stat exam 3 (ch. 9)

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Using an α = .04, a confidence interval for a population proportion is determined to be .65 to .75. If the level of significance is decreased, the interval for the population proportion:

becomes wider

When constructing a confidence or a prediction interval to quantify the relationship between two quantitative variables, the appropriate degrees of freedom are:

n-2

In a regression analysis, if SSE = 200 and SSR = 300, then the coefficient of determination is:

0.6 If SSE = 200 and SSR = 300, then the coefficient of determination is .6. The value of r2 = SSR/(SSE + SSR) = 300/(200 + 300) = .6

A researcher is interested to determine the average age at which people obtain their first credit card. If past information shows a mean of 22 years and a standard deviation of 2 years, what size sample should be taken so that at 95% confidence the margin of error will be 3 months or less?

246 (1.96)^2(2)^2/.25^2

The following information regarding the number of semester hours taken from random samples of day and evening students is provided. xbar 15.5 8.1 s 2.4 2.75 n 36 65 Find a 95% confidence interval estimate for the difference between the mean semester hours taken by the two groups of students.

6.354 to 8.446 (15.5 - 8.1) +/- 1.990(sq root of (2.4^2 / 36) + (2.75^2 / 65))

When computing the sample size needed to estimate a proportion within a given margin of error for a specific confidence level, what planning value of p* should be used when no estimate of p* is available?

.50

Sales data from a family-owned store shows that 78% of a random sample of 300 customers pay using a credit card. Compute the 99% confidence interval for the population proportion.

.72 to .84 .78 +- 2.576 sqrt(.78(1-.78)/300)

The tests of significance in regression analysis are based on assumptions about the error term ɛ. One such assumption is that the error term ɛ is a random variable with a mean or expected value of:

The tests of significance in regression analysis are based on assumptions about the error term ɛ . One such assumption is that the variance of ɛ, denoted by 𝝈2, is:

the same for all values of x

What is the probability of making a Type I error?

the significance level, α

In a regression analysis, an outlier will always increase:

the value of the correlation

For a two-tail test, the p-value is the probability of obtaining a value for the test statistic as

unlikely as that provided by the sample

The matched sample design often leads to a smaller sampling error than the independent sample design. The primary reason is that in a matched sample design,

variation between subjects is eliminated because the same subjects are used for both treatments

Regarding hypothesis tests about p1 - p12, the pooled estimate of p is a

weighted average of p(bar)1 an p(bar)2

What is the symbol for the sample mean?

x̄

Whenever the probability of making a Type II error has not been determined and controlled, only two conclusions are possible. We either reject H0 or

do not reject Ho

The model developed from sample data that has the form yhat = b0 + b1x is known as the:

estimated regression equation

If a significant relationship exists between x and y and the coefficient of determination shows that the fit is good, the estimated regression equation should be useful for:

estimation and prediction

For a fixed confidence level and population standard deviation, if we would like to cut our margin of error in half, we should take a sample size that is:

four times as large as the original sample size.

The average gasoline price of one of the major oil companies has been hovering around $2.20 per gallon. Because of cost reduction measures, it is announced that there will be a significant reduction in the average price over the next month. In order to test this belief, we wait one month, then randomly select a sample of 36 of the company's gas stations. We find that the average price for the stations in the sample was $2.15. The standard deviation of the prices for the selected gas stations is $0.10. Given that the test statistic for this sample is t = - 3, determine the p-value.

p-value = .002

In a random sample of 400 registered voters, 120 indicated they plan to vote for Trump for President. Determine a 95% confidence interval for the proportion of all the registered voters who will vote for Trump.

(.26, .34) .3 +- sqrt(.3(1-.3)/ 400)

A sample of 100 footballs showed an average air pressure of 13 psi. The standard deviation of the population is known to be .25 psi. What is the standard error of the mean?

.025 .25/sqrt(100)

Male college basketball players have to weigh-in during season, and this information is published. We can, therefore, know the standard deviation of the entire population. Suppose we do not know the population mean and wanted to estimate it. Suppose we took a random sample of 25 male college basketball players and recorded their weights. The sample mean was found to be 220 lbs. The population standard deviation was 5 lbs. What is the standard error of the mean?

1 5/sqrt(25)

The daily production rates for a sample of factory workers before and after a training program are shown below. Let d = After - Before. worker before after 1 6 9 2 10 12 3 9 10 4 8 11 5 7 9 6 7 7 7 6 8 8 10 9 We want to determine if the training program is effective. Compute sd.

1.414

1.5

Suppose a 95% confidence interval, based upon a sample of size 25, for the mean number of hours of sleep that college students get per night was 5 to 8 hours. How many students should be surveyed in order to cut the width of the interval down from 3 hours to 1.5 hours?

100

Tterm-19he following results are for independent random samples taken from two populations xbar 16 12 s 14 2 n 140 160 We are not willing to assume that the population standard deviations are equal. What is the appropriate degrees of freedom?

143

A random sample of 144 observations has a mean of 20, a median of 21, and a mode of 22. The population standard deviation is known and is equal to 4.8. The 95.44% confidence interval for the population mean is:

19.200 to 20.800.

In order to determine an interval for the mean of a population with unknown standard deviation, a sample of 24 items is selected. The mean of the sample is determined to be 23. The number of degrees of freedom for reading the t value is:

A statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups as they could. The 10 randomly selected students averaged 15 pushups per person with a standard deviation of 9 pushups. Suppose the distribution of the population of number of pushups that can be done is approximately normal. If we would like to capture the population mean with 95% confidence, the margin of error would be:

2.262(9/sqrt(10))

In an interval estimation for a proportion of a population, the z value for 99% confidence is:

2.576

2.576 2.576(5/sqrt(25))

The z value for a 99% confidence interval estimation is:

2.58

2.846 s/sqrt(n)9/sqrt(10)

220 +- 2.576(5/sqrt(25))

The t value for a 99% confidence interval estimation based upon a sample of size 10 is:

3.250

A researcher is interested to determine the average number of years new teachers remain in the classroom. If past information shows a standard deviation of 5 years, what size sample should be taken so that at 95% confidence the margin of error will be 6 months or less?

385 (1.96)^2(5)^2/.5^2

A local health center noted that in a sample of 400 patients 80 were referred to them by the local hospital. What size sample would be required to estimate the proportion of hospital referrals with a margin of error of .04 or less at 95% confidence?

385 n=(z a/2)p(1-p)/E^2(1.96)^2*(.2)(1-.2)/.04^2

The following shows the monthly sales in units of six salespersons before and after a bonus plan was introduced. Let the difference "d" be: d = After - Before. salesperson before after 1 90 94 2 84 82 3 84 90 4 70 76 5 80 79 6 80 85 We would like to calculate a 99% confidence interval to estimate the mean difference in monthly sales for all sales individuals at this company. What is the margin of error?

4.032 x (3.58 / sq root 6)

An elementary school teacher asked a random sample of 12 of her students what their favorite number was. Assume the population of responses would follow a normal distribution. The students stated that their favorite numbers are: 2 10 7 4 0 5 6 4 4 6 1 100 Suppose the student who said "100" was left out of the data set. Create a revised 95% confidence interval for μ.

4.45 +- 2.228 (2.84/sqrt(11))

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customers to checkout was 3 minutes. It is known that the standard deviation of the population of checkout times is 1 minute. With a .95 probability, the sample mean will provide a margin of error of .196. If we wanted to cut this margin of error in half, how many customers would we need to include in our sample?

400 (1.96)^2(1)^2/.098^2

An analyst for a cell phone company would like to know the average age at which people obtain their first cell phone. Past records show a mean of 14 years and a standard deviation of 8 years. What sample size should be taken so that at 99% confidence the margin of error will be 1 year or less?

425 n= z^2*sigma^2/E^2=(2.576)^2*(8)^2/1^2

5 n-1

The CEO of a company wants to estimate the percent of employees who use company computers to go on Facebook during work hours with 95% confidence. He selects a random sample of 150 of the employees and finds that 53 of them logged onto Facebook that day. The CEO would like to cut the margin of error in half without changing the confidence level. How large of a sample size is needed?

600 To cut the margin of error in half, the sample size must quadruple

In an analysis of variance problem involving three treatments and 10 observations per treatment, SSE = 399.6. The MSE for this situation is _____. A) 14.8 B) 30.0 C) 13.32 D) 133.2

A) 14.8

The F ratio in a completely randomized ANOVA is the ratio of _____. A) MSE/MSTR B) MSTR/MSE C) MST/MSE D) MSE/MST

B) MSTR/MSE

The independent variable of interest in an ANOVA procedure is called _____. A) a factor B) a partition C) either a partition or a treatment D) a treatment

A) a factor

An experimental design that permits statistical conclusions about two or more factors is a: A) factorial design. B) randomized block design. C) randomized design. D) completely randomized design.

A) factorial design.

Which of the following describe a Type II Error?

Accept Ho when it's false

An experimental design that allows simultaneous conclusions about two or more factors is called a: A) randomized block experiment. B) factorial experiment. C) matched samples experiment. D) completely randomized experiment.

B) factorial experiment.

In an experimental design, another word used for the independent variable is the: A) level. B) design. C) factor. D) treatment.

C) factor.

The process of using the same or similar experimental units for all treatments is called: A) confounding. B) randomization. C) stratification. D) blocking.

D) blocking.

In ANOVA procedures, the between-treatments approach provides a good estimate of σ^2 only when: A) there are 3 or more treatments. B) the sample size of each treatment group is 30 or more. C) the alternative hypothesis is true. D) the null hypothesis is true.

D) the null hypothesis is true.

The ANOVA procedure is a statistical approach for determining whether the means of _____. A) two samples are equal B) more than two samples are equal C) two or more samples are equal D) two or more populations are equal

D) two or more populations are equal

The following data show the results of an aptitude test and the grade point average of 10 students. GPA: 1.8, 2.3, 2.6, 2.4, 2.8, 3.0, 3.4, 3.2, 3.6, 3.8 Aptitude Test Scores: 26, 31, 28, 30, 34, 38, 41, 44, 40, 43 At 95% confidence, test to determine if the model is significant (Perform an F test). What is the test statistic and p-value ?

F = 39.07 and p-value = .0002 F = MSR/MSE. The p-value is based on an F distribution with 1 degree of freedom in the numerator and n − 2 degrees of freedom in the denominator. MSR = SSR/p = sum of(yhat - ybar)^2/p MSE = SSE/n-p-1 = sum of (yi-yhati)^2)/n-p-1 See paper.

A doctor would like to know if men and women got the same amount of sleep per night or if women tended to get less sleep than men. He took a random sample of 100 of his male and 100 of his female patients and asked them how many hours of sleep they got, per night, on average. The women slept an average of 6.75 hours and the men slept an average of 7.5 hours. Suppose we also knew the population standard deviations to be 1.25 hours and 1.5 hours for men and women, respectively. Formulate the null and alternative hypotheses to test whether women sleep less than men do, on average.

H0 : Um - Uw = 0 Ha : Um - Uw > 0

The average hourly wage of computer programmers with 2 years of experience has been $21.80. Because of high demand for computer programmers, it is believed there has been a significant increase in the average wage of computer programmers. To test whether or not there has been an increase, the correct hypotheses to be tested are

H0 : u <= 21.80 Ha : u > 21.80

Which of the following null hypotheses cannot be correct?

H0 : u not = 10

A local entrepreneur would like to know if those who live in an urban or rural community are more likely to buy a real Christmas tree. He takes a random sample of 100 people who reside in the city and a separate random sample of 100 people who live in the country and asks them if they buy a real tree at Christmas time. Of the urban participants, 22 buy a real tree. Of the rural participants, 28 buy a real tree. Do we have enough evidence at the α = 0.05 level to conclude that the proportion of people who buy a real Christmas tree is greater for those living in rural than urban communities?

No! The p-value is greater than 0.05 so we do not have enough evidence to conclude that the proportion of people who buy a real Christmas tree is greater for those living in rural than urban communities.

A company runs two production lines, A and B, when packaging canned vegetables. If a can has a dent or any visual imperfection it is considered to be defective. From production line A, a random sample of 200 cans are selected, and it is determined that 12 are defective. From production line B, a random sample of 300 cans are selected, and it is determined that 21 are defective. Develop a 90% confidence interval for the difference between the two population proportions. Based upon the calculated confidence interval, do we have evidence to conclude that the proportion of defective cans differs for the two production lines?

No. The value of zero is contained in the 90% confidence interval, so we do not believe that there is a difference in the proportion of defective cans differs for the two production lines.

Which of the following describe a Type I Error?

Reject Ho when it's true

σ known

The case when historical data or other information provide a good value for the population standard deviation prior to taking a sample. The interval estimation procedure uses this known value of σ in computing the margin of error.

confidence level

The confidence associated with an interval estimate. For example, if an interval estimation procedure provides intervals such that 95% of the intervals formed using the procedure will include the population parameter, the interval estimate is said to be constructed at the 95% confidence level. for an interval estimate.

Practical Signficance

The real-world impact the result of statistical inference will have on business decisions.

margin of error

The ± value added to and subtracted from a point estimate in order to develop an interval estimate of a population parameter.

The chi-squared distribution is a family of curves that are a.approximately normal. b.skewed to the right. c.bimodal. d.uniformly distributed.

b.skewed to the right.

Yes! The p-value is less than 0.05, so we have enough evidence to conclude that the training program is effective.

The following information regarding the number of semester hours taken from random samples of day and evening students is provided. xbar 15.5 8.1 s 2.4 2.75 n 36 65 Is there a significant difference in the mean semester hours taken by the two groups of students at the α = 0.05 level?

Yes! the p-value is less than the significance level of 0.05

Based on the sample evidence below, we want to test the hypothesis that population A has a larger variance than population B. Sample A Sample B s² 12.1 5 n 11 10 Which of the following gives the correct test statistic? a. F = 12.1/5 b. F = 5/12.1 c. F = 12.1²/5² d. F = 5²/12.1²

a. F = 12.1/5

An egg packing company has stated that the standard deviation of the weights of their grade A large eggs is 0.07 ounces or less. The sample variance for 51 eggs was 0.0065 ounces. What are the appropriate null and alternative hypotheses? a. H₀: 𝜎² ≤ 0.07, Hɑ: 𝜎² > 0.07 b. H₀: 𝜎² ≥ 0.07, Hɑ: 𝜎² < 0.07 c. H₀: 𝜎² < 0.07, Hɑ: 𝜎² ≥ 0.07 d. H₀: 𝜎² > 0.07, Hɑ: 𝜎² ≤ 0.07

a. H₀: 𝜎² ≤ 0.07, Hɑ: 𝜎² > 0.07

A sample of 25 elements is selected to estimate a 98% confidence interval for the variance of the population. The chi-square values to be used for this interval estimation are a.10.856 and 42.980. b.12.401 and 39.364. c.13.848 and 36.415. d.15.695 and 33.196.

a.10.856 and 42.980.

In interval estimation, as the sample size becomes larger, the interval estimate:

becomes narrower.

We can use the chi-square distribution to develop interval estimates and conduct hypothesis tests about a population variance as long as the data comes from a.a simple random sample selected from a normal population. b.a stratified random sample selected from a unimodal population. c.a systematic random sample selected from a right skewed population. d.a simple random sample selected from a right skewed population.

a.a simple random sample selected from a normal population.

The sampling distribution of the quantity (n-1)(s²)/𝜎² follows a a.chi-square distribution. b.normal distribution. c.F distribution. d.t distribution.

a.chi-square distribution.

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

Which of the following statements is false? a. ŷ is the point estimator of E(y) , the mean value of y for a given value of x. b. Regression analysis can be interpreted as a procedure for establishing a cause-and-effect relationship between variables. c. In practice, parameter values are not known and must be estimated using sample data. d. In the estimated simple linear regression equation, b0 is the y-intercept and b1 is the slope.

b. Regression analysis can be interpreted as a procedure for establishing a cause-and-effect relationship between variables. Regression analysis CANNOT be interpreted as a procedure for establishing a cause-and-effect relationship between variables.

A machine produces pipes used in airplanes. The average length of the pipe is 16 inches. The acceptable variance for the length is 0.3 inches. A sample of 25 pipes was taken. The average length in the sample was 15.95 inches with a variance of 0.4 inches. Which of the following gives the 95% confidence interval estimate of the population standard deviation? a. √(24)(0.3)/39.364 ≤ 𝜎 ≤ √(24)(0.3)/12.401 b. √(24)(0.4)/39.364 ≤ 𝜎 ≤ √(24)(0.4)/12.401 c. (24)(0.3²)/39.364 ≤ 𝜎 ≤ (24)(0.3²)/12.401 d. (24)(0.4²)/39.364 ≤ 𝜎 ≤ (24)(0.4²)/12.401

b. √(24)(0.4)/39.364 ≤ 𝜎 ≤ √(24)(0.4)/12.401

An egg packing company has stated that the standard deviation of the weights of their grade A large eggs is 0.07 ounces or less. The sample variance for 51 eggs was 0.0065 ounces. Calculate the test statistic appropriate for testing this claim. a. χ² = √(51-1)(0.0065²)/(0.07²) b. χ² = √(51-1)(0.07²)/(0.0065²) c. χ² = (51-1)(0.0065²)/(0.07²) d. χ² = (51-1)(0.07²)/(0.0065²)

c. χ² = (51-1)(0.0065²)/(0.07²)

A sample of 20 elements is selected to estimate a 90% confidence interval for the variance of the population. The chi-square values to be used for this interval estimation are a.7.633 and 36.191. b.8.907 and 32.852. c.10.117 and 30.144. d.11.651 and 27.204.

c.10.117 and 30.144. This is based upon 19 degrees of freedom and right tail probabilities of 0.05 and 0.95.

The chi-square value for a one-tailed test (lower tail) when the level of significance is 0.1 and the sample size is 15 is a.21.06. b.23.69. c.7.79. d.6.57.

c.7.79. (Use Chi-Square table at intersection of 14 degrees of freedom and an upper tail probability of 0.90)

The ratio of sample variances provides the F test statistic F = s₁²/s₂² provided that which of the following assumptions is met? a.Both populations must have distributions that are right skewed. b.The sample size for each group must be 30 or more. c.Both populations must have a normal distribution. d.The sample size for each group must be 10 or more.

c.Both populations must have a normal distribution.

The sampling distribution of the ratio of independent sample variances extracted from two normal populations with equal variances follows the a.chi-square distribution. b.normal distribution. c.F distribution. d.t distribution.

c.F distribution.

To avoid the problem of not having access to Tables of F distribution with values given for the lower tail, the numerator of the test statistic should be the one with a.the larger sample size. b.the smaller sample size. c.the larger sample variance. d.the smaller sample variance.

c.the larger sample variance.

In making comparisons about the two population variances, we will be using data collected from a.two independent stratified samples. b.paired samples from two distinct populations. c.two independent random samples. d.paired samples from one population classified according to two characteristics.

c.two independent random samples.

When studying the relationship between two quantitative variables, an interval estimate of the mean value of y for a given value of x is called a(n):

confidence interval

The value of F₀.₀₁ with 10 numerator and 20 denominator degrees of freedom is a.2.39. b.2.94. c.2.91. d.3.37.

d.3.37. (Use numerator/denominator table)

Because the F statistic is constructed with the larger sample variance in the numerator, the value of the test statistic will always a.be in the upper tail of the distribution. b.have a value of 1 or more. c.be positive. d.All of the above.

d.All of the above.

d.F = 6.05 F = 12.8²/5.2² = 6.05

Which of the following is the point estimator of the population variance? a.σ b.s c.σ² d.s²

d.s²

Observations with extreme values for the independent variables are called:

high leverage points

In general, higher confidence levels provide larger confidence intervals. One way to have high confidence and a small margin of error is to:

increase the sample size.

We can reduce the margin of error in an interval estimate of p by doing any of the following except:

increasing the planning value p* to .5.

The tests of significance in regression analysis are based on assumptions about the error term ɛ. One such assumption is that the values of ɛ are:

independent

Regarding inferences about the difference between two population means, the alternative to the matched sample design, as covered in the textbook, is

independent samples

An observation that has a strong influence or effect on the regression results is called a(n):

influential observation

An approximate value of a population parameter that provides limits and believed to contain the value of the parameter is known as the

interval estimate

The tests of significance in regression analysis are based on several assumptions about the error term ɛ. Additionally, we make an assumption about the form of the relationship between x and y. We assume that the relationship between x and y is:

linear

The value added and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the:

margin of error.

A researcher recruits 25 people to participate in a study on alcohol consumption and its interactions with Tylenol. The 25 participants had to come to a check-in center every day at 7am for one week. They were given various amounts of alcohol. Each day, each participant would flip a coin to determine if they also took Tylenol with their alcohol. They found that their BAC was 25% higher on days when they were given Tylenol with their alcohol than when they drank alcohol alone. This is an example of a

matched sample design

Suppose we are constructing an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown. Suppose also that it can be assumed the two populations have equal variances. If n1 is the size of sample 1 and n2 is the size of sample 2, we must use a t distribution with

n1 + n2 - 2 degrees of freedom

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

n1 and n2 can be of different sizes

The sampling distribution of p̅1 - p̅2 is approximated by a normal distribution when

n1p1, n1(1 - p1), n2p2, and n2(1 - p2) are all greater than or equal to 1

The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation is called a(n):

residual

Graphical representation of the residuals that can be used to determine whether the assumptions made about the regression model appear to be valid is called a:

residual plot

Suppose we have a t distribution based upon two sample means with unknown population standard deviations which we are unwilling to assume are equal. When we calculate the appropriate degrees of freedom we should

round the calculated degrees of freedom down to the nearest integer

For the case where σ is unknown, what statistic is used to estimate σ?

When σ is unknown, what is used to estimate σ?

The margin of error in an interval estimate of the population mean is a function of all of the following except the:

sample mean.

An F test, based on the F probability distribution, can be used to test for:

significance in regression

Applications of hypothesis testing that only control for the Type I error are called

significance tests

A doctor would like to know if men and women got the same amount of sleep per night or if women tended to get less sleep than men. He took a random sample of 100 of his male and 100 of his female patients and asked them how many hours of sleep they got, per night, on average. The women slept an average of 6.75 hours and the men slept an average of 7.5 hours. Suppose we also knew the population standard deviations to be 1.25 hours and 1.5 hours for men and women, respectively. What is the standard error of the difference in the means?

sq root of ((1.5^2 / 100) + (1.25^2 / 100))

The standard error of x(bar1) - x(bar2) is given by

sq root of ((standard dev. 1 ^2 / n1) + (standard dev. 2 ^2 / n2))

Following is a portion of the computer output for a regression analysis relating y = number of people who use the public pool to x = the outside temperature. Predictor Coef Stdev t-ratio P Constant. 57.912 5.674 10.21 0.000 Temp 0.81138 0.09038 8.98 0.000 s=1.198 R-sq=94.2% R-sq(adj)=93% State the test statistic and p-value used to determine whether the number of people who use the public pool is related to the outside temperature.

t = 8.98 and p-value = .000 The test statistic and p-value are found in the computer output. They are t = 8.98 and p-value = .000.

The following data represent a company's yearly sales volume and its advertising expenditure over a period of 8 years. Advertising Expenses: 32, 33, 35, 34, 36, 37, 39, 42 Sales: 15, 16, 18, 17, 16, 19, 19, 24 Use the least squares method to develop the estimated regression equation.

yhat = -10.42 + 0.79x yhat = b0 + b1x b1 = sum of (xi - xbar)(yi - ybar) / sum of (xi -xbar)^2 b1 = 0.789 b0 = ybar - b1x b0 = 18 - 0.789(xbar) b0 = 18 - 0.79(36) b0 = -10.42 yhat = -10.42 + 0.79x

yhat = 57.912 + 0.81138x. yhat = b0 + b1x b0 can be located under coef for the constant b1 can be located under coef for the temp

In a regression analysis, the error term ε is a random variable with a mean or expected value of

zero

What is the symbol for the population mean?

(0.07 - 0.06) +/- 1.645 (sq root of ((.07)(.93) / 300) + ((.06)(.94) / 200)

A doctor would like to know if men and women got the same amount of sleep per night or if women tended to get less sleep than men. He took a random sample of 100 of his male and 100 of his female patients and asked them how many hours of sleep they got, per night, on average. The women slept an average of 6.75 hours and the men slept an average of 7.5 hours. Suppose we also knew the population standard deviations to be 1.25 hours and 1.5 hours for men and women, respectively. Find a 90% confidence interval for the difference in the population means.

(0.43, 1.07) (7.5 - 6.75) +/- 1.645(sq root of (1.5^2 / 100) + (1.25^2 / 100))

The following shows the monthly sales in units of six salespersons before and after a bonus plan was introduced. Let the difference "d" be: d = After - Before. salesperson before after 1 90 94 2 84 82 3 84 90 4 70 76 5 80 79 6 80 85 Calculate a 99% confidence interval to estimate the mean difference in monthly sales for all salespersons before and after the bonus plan was introduced.

-2.9 to 8.9

A doctor would like to know if men and women got the same amount of sleep per night or if women tended to get less sleep than men. He took a random sample of 100 of his male and 100 of his female patients and asked them how many hours of sleep they got, per night, on average. The women slept an average of 6.75 hours and the men slept an average of 7.5 hours. Suppose we also knew the population standard deviations to be 1.25 hours and 1.5 hours for men and women, respectively. What is the p-value of the test? Should the null hypothesis be rejected?

.000061 The null hypothesis should be rejected.

The CEO of a company wants to estimate the percent of employees who use company computers to go on Facebook during work hours with 95% confidence. He selects a random sample of 150 of the employees and finds that 53 of them logged onto Facebook that day. What is the estimate of the standard error of the proportion ?

.039 sigma sub p bar = sqrt(.353(1-.353)/ 150)

A sample of 100 footballs showed an average air pressure of 13 psi. The standard deviation of the population is known to be .25 psi. With a .90 probability, the margin of error is approximately equal to:

.041 MOE= Z*(sigma/sqrt(n))1.645*(.25/sqrt(100))

.076 1.96 sqrt(.353(1-.353)/150)

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the population of checkout times is one minute. The standard error of the mean is equal to:

.100 1/sqrt(100)

.196 1.96(1/sqrt(100))

The CEO of a company wants to estimate the percent of employees who use company computers to go on Facebook during work hours with 95% confidence. He selects a random sample of 150 of the employees and finds that 53 of them logged on to Facebook that day. What is the point estimate of the proportion of the population who logged on to Facebook that day?

.35 53/150

The CEO of a company wants to estimate the percent of employees who use company computers to go on Facebook during work hours with 95% confidence. He selects a random sample of 150 of the employees and finds that 53 of them logged onto Facebook that day. Compute the 95% confidence interval for the population proportion.

.35+- 1.96*sqrt(.35(1-.35)/150)

A company runs two production lines, A and B, when packaging canned vegetables. If a can has a dent or any visual imperfection it is considered to be defective. From production line A, a random sample of 200 cans are selected, and it is determined that 12 are defective. From production line B, a random sample of 300 cans are selected, and it is determined that 21 are defective. What is the point estimate of the difference between the two population proportions?

0.01 (21/300) - (12/200) = 0.01

0.09038 If you look at the chart, locate b1 or temp and then locate the standard deviation, which gives you 0.09038.

0.16

A doctor would like to know if men and women got the same amount of sleep per night or if women tended to get less sleep than men. He took a random sample of 100 of his male and 100 of his female patients and asked them how many hours of sleep they got, per night, on average. The women slept an average of 6.75 hours and the men slept an average of 7.5 hours. Suppose we also knew the population standard deviations to be 1.25 hours and 1.5 hours for men and women, respectively. What is the point estimate for the difference between the mean number of hours that women and men sleep?

0.75 7.5 - 6.75 = 0.75

The following information regarding the number of semester hours taken from random samples of day and evening students is provided. xbar 15.5 8.1 s 2.4 2.75 n 36 65 What is the margin of error for a 95% confidence interval estimate for the difference between the mean semester hours taken by the two groups of students?

1.990 x (sq root of (2.4^2 / 36) + (2.75^2 / 65))

A professor would like to estimate the average number of hours his students spend doing work and studying throughout the semester for the course he teaches. He wants to estimate μ with 99% confidence and with a margin of error of at most 2 hours. From past experience, he believes that the standard deviation of the number of hours students spent is 8 hours. How many students need to be surveyed to meet these requirements?

107 (2.576)^2(8)^2/2^2

An elementary school teacher asked a random sample of 12 of her students what their favorite number was. Assume the population of responses would follow a normal distribution. The students stated that their favorite numbers are: 2 10 7 4 0 5 6 4 4 6 1 100 What is the appropriate degrees of freedom to use when calculating a 95% confidence interval for μ ?

11 n-1

The sample size needed to provide a margin of error of 2 or less with 95% confidence when the population standard deviation is equal to 11 is:

117 (1.96)^2(11)^2/2^2

12.42 +- 2.201(27.7/sqrt(12))

A sample of 100 footballs showed an average air pressure of 13 psi. The standard deviation of the population is known to be .25 psi. The 99% confidence interval for the true mean air pressure for all footballs is:

12.936 to 13.06413 +- 2.576(.25/sqrt(100))

Following is a portion of the computer output for a regression analysis relating y = number of people who use the public pool to x = the outside temperature. Predictor Coef Stdev t-ratio P Constant. 57.912 5.674 10.21 0.000 Temp 0.81138 0.09038 8.98 0.000 s=1.198 R-sq=94.2% R-sq(adj)=93% Predict approximately how many people will use the public pool in a day when the temperature is 90 degrees.

131 To predict how many people will use the public pool in a day when the temperature is 90 degrees, substitute 90 for x in the regression equation. yhat = 57.912 + 0.81138(90) = 131 yhat = b0 + b1x yhat = 57.912 + 0.81138(90) yhat = 131

The following information regarding the number of semester hours taken from random samples of day and evening students is provided. xbar 15.5 8.1 s 2.4 2.75 n 36 65 We would like to know if the difference in the mean semester hours taken by the two groups of students is statistically significant at the α = 0.05 level. What is the test statistic?

14.08 t = 15.5 - 8.1 / (sq root of (2.4^2 / 36) + (2.75^2 / 65)) = 14.08

The following results are for independent random samples taken from two populations xbar 6 52 s 4 12 n 40 60 We are not willing to assume that the population standard deviations are equal. What is the appropriate degrees of freedom?

The following data show the results of an aptitude test and the grade point average of 10 students. GPA: 1.8, 2.3, 2.6, 2.4, 2.8, 3.0, 3.4, 3.2, 3.6, 3.8 Aptitude Test Scores: 26, 31, 28, 30, 34, 38, 41, 44, 40, 43 The t test for a significant relationship between GPA and Aptitude Test Score is based on a tdistribution with _____ degrees of freedom.

8 A t test for slope is based on a t distribution with n - 2 degrees of freedom. The sample size for this problem is n = 10, so there are 8 degrees of freedom.

A statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups as they could. The 10 randomly selected students averaged 15 pushups per person with a standard deviation of 9 pushups. Suppose the distribution of the population of number of pushups that can be done is approximately normal. The 95% confidence interval for the true mean number of pushups that can be done is:

8.56 to 21.4415 +- 2.262(9/sqrt(10))

The following information regarding the number of semester hours taken from random samples of day and evening students is provided. xbar 15.5 8.1 s 2.4 2.75 n 36 65 What is the appropriate degrees of freedom for calculating a 95% confidence interval for the difference between the mean semester hours taken by the two groups of students?

= 0.25 p = (100(.22) + 100(.28)) / (100 + 100) = 0.25

t distribution

A family of probability distributions that can be used to develop an interval estimate of a population mean whenever the population standard deviation σ is unknown and is estimated by the sample standard deviation s.

degrees of freedom

A parameter of the t distribution. When the t distribution is used in the computation of an interval estimate of a population mean, the appropriate t distribution has n − 1 degrees of freedom, where n is the size of the sample.

A t distribution should be used because σ is unknown.

The Nestle Corporation wants to increase the productivity of its line workers. Four different programs have been suggested to increase the productivity. Twenty employees, making up a sample, have been randomly assigned to one of the four programs, and their output for a day's work has been recorded. The results are given below. Program A: 150, 130, 120, 180, 145 Program B: 150, 120, 135, 160, 110 Program C: 185, 220, 190, 180, 175 Program D: 175, 150, 120, 130, 175 The ANOVA procedures provide enough evidence to conclude that the population means are not all equal. When carrying out the Fisher's LSD procedure to determine which mean is different from the others, using α = 0.05, what is the comparisonwise Type I error rate? A) 0.05 B) 0.20 C) 0.03 D) 0.01

A) 0.05

The Nestle Corporation wants to increase the productivity of its line workers. Four different programs have been suggested to increase the productivity. Twenty employees, making up a sample, have been randomly assigned to one of the four programs, and their output for a day's work has been recorded. The results are given below. Program A: 150, 130, 120, 180, 145 Program B: 150, 120, 135, 160, 110 Program C: 185, 220, 190, 180, 175 Program D: 175, 150, 120, 130, 175 The ANOVA procedures provide enough evidence to conclude that the population means are not all equal. When carrying out the Fisher's LSD procedure to determine which mean is different from the others, using α = 0.05, what is the experimentwise Type I error rate? A) 0.26 B) 0.05 C) 0.01 D) 0.20

A) 0.26 1 - 0.95^6 = 0.2649 ≈ 0.26 *there are 6 different piecewise comparisons to make when carrying out the Fisher's LSD procedure, hence raising 0.95 to the 6th power.

An ANOVA procedure is used for data obtained from five populations. Five samples, each comprised of 10 observations, were taken from the five populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are _____. A) 4 and 45. B) 5 and 10. C) 4 and 49. D) 4 and 9.

A) 4 and 45. k - 1 => 5 - 1 = 4 n - k => 50 - 5 = 45

An experiment was designed in order to determine how to make the ideal steak. One factor that studied was how long the steaks marinated before being cooked: 30 minutes, 1 hour, 2 hours, and 4 hours. Another factor was the method used for cooking the steak: charcoal grill, gas grill, oven, or pan seared. Assume that 5 steaks will be cooked using each of the treatment combinations. Replication is a term used within experimental design. How many replications are used in this experimental design? A) 5 B) 20 C) 16 D) 80

A) 5

Six observations were selected from each of three populations. The data obtained is shown below. Sample 1: 31, 28, 34, 32, 26, 29 Sample 2: 37, 32, 34, 24, 32, 33 Sample 3: 37, 31, 32, 39, 30, 35 What type of experimental design was used? A) Completely randomized design B) Randomized design C) Factorial Design D) Randomized block design

A) Completely randomized design

The marketing department of a company has assigned three different boxes for its product. It wants to determine which box will produce the largest amount of sales. Each box will be test marketed in five different stores for a period of a month. The information on sales is given below. Box 1: Store 1 = 210, Store 2 = 230, Store 3 = 190, Store 4 = 180, Store 5 = 190 Box 2: Store 1 = 195, Store 2 = 170, Store 3 = 200, Store 4 = 190, Store 5 = 193 Box 3: Store 1 = 295, Store 2 = 275, Store 3 = 290, Store 4 = 275, Store 5 = 265 What type of design does this experiment have? A) Randomized block design B) Completely randomized design C) Fisher's LSD design D) Cluster sampling design

A) Randomized block design

The process of allocating the total sum of squares and degrees of freedom into their corresponding sources is called: A) partitioning. B) factoring. C) replicating. D) blocking.

A) partitioning.

interval estimate

An estimate of a population parameter that provides an interval believed to contain the value of the parameter. For the interval estimates in this chapter, it has the form: point estimate ± margin of error.

The estimated regression equation, yhat = -10.42 + 0.79x , can be used to predict a company's sales volume (y), in millions, based upon its advertising expenditure (x), in $10,000s. What is the company's predicted sales volume if they spend $500,000 on advertising?

Approximately $29 million The tricky thing about this problem is to know what to substitute into the regression equation for x. $500,000 is (50)(10,000), so x = 50. Substituting x = 50 into the regression equation gives ŷ = 29.08, which is in millions of dollars.

An experiment was designed in order to determine how to make the ideal steak. One factor that was studied was how long the steaks marinated before being cooked: 30 minutes, 1 hour, 2 hours, and 4 hours. Another factor was the method used for cooking the steak: charcoal grill, gas grill, oven, or pan seared. How many total treatment combinations were studied? A) 8 B) 16 C) 4 D) 12

B) 16

In a completely randomized design involving three treatments, the following information is provided: Sample Size: Treatment 1 = 5, Treatment 2 = 10, Treatment 3 = 5 Sample Mean: Treatment 1 = 4, Treatment 2 = 8, Treatment 3 = 9 The overall mean for all the treatments is: A) 7.00 B) 7.25 C) 6.67 D) 4.89

B) 7.25 (4)(5) + (8)(10) + (9)(5) / 5+10+5 = 145 / 20 = 7.25

Which of the following is not a required assumption for the analysis of variance? A) The variance associated with the random variable must be the same for each population. B) The populations have equal means. C) The random variable of interest for each population has a normal probability distribution. D) At least two populations are under consideration.

B) The populations have equal means.

Which of the following options is not a required assumption for the use of ANOVA procedures? A) The variance of the response variable is the same for all of the populations. B) The sample size of each group must be 30 or more. C) For each population, the response variable is normally distributed. D) The observations must be independent.

B) The sample size of each group must be 30 or more.

An experimental design in which the treatments are randomly assigned to the experimental units is called a: A) randomized block design. B) completely randomized design. C) simple random sample design. D) matched samples design.

B) completely randomized design.

The test statistic for the Fisher's LSD test follows the: A) z distribution. B) t distribution. C) x^2 distribution. D) F distribution.

B) t distribution.

ANOVA procedures can be used to determine: A) whether the population standard deviations are equal. B) whether the population means are equal. C) whether the population variances are equal. D) whether the population sizes are equal.

B) whether the population means are equal.

The following data show the results of an aptitude test and the grade point average of 10 students. GPA: 1.8, 2.3, 2.6, 2.4, 2.8, 3.0, 3.4, 3.2, 3.6, 3.8 Aptitude Test Scores: 26, 31, 28, 30, 34, 38, 41, 44, 40, 43 If GPA and Aptitude Test Scores are linearly related, which of the following must be true?

B1 is not equal to 0????????????????????????????????

The Nestle Corporation wants to increase the productivity of its line workers. Four different programs have been suggested to increase the productivity. Twenty employees, making up a sample, have been randomly assigned to one of the four programs, and their output for a day's work has been recorded. The results are given below. Program A: 150, 130, 120, 180, 145 Program B: 150, 120, 135, 160, 110 Program C: 185, 220, 190, 180, 175 Program D: 175, 150, 120, 130, 175 State the null and alternative hypotheses. A) H0: x̄ 1 = x̄ 2 = x̄ 3 = x̄ 4 ; Ha: Not all of x̄ 1, x̄ 2, x̄ 3, and x̄ 4 are equal. B) H0: x̄ 1 = x̄ 2 = x̄ 3 = x̄ 4 = x̄ 5 ; Ha: Not all of x̄ 1, x̄ 2, x̄ 3, x̄ 4, and x̄ 5 are equal. C) H0: μ1 = μ2 = μ3 = μ4 ; Ha: Not all of μ1, μ2, μ3, and μ4 are equal. D) H0: μ1 = μ2 = μ3 = μ4 = μ5 ; Ha: Not all of μ1, μ2, μ3, μ4, and μ5 are equal.

C) H0: μ1 = μ2 = μ3 = μ4 ; Ha: Not all of μ1, μ2, μ3, and μ4 are equal.

An ANOVA procedure is used for data obtained from five populations. Five samples, each comprised of 10 observations, were taken from five populations. The null hypothesis for this ANOVA problem is: A) H0: μ1 = μ2 = μ3 = μ4. B) H0: μ1 = μ2 = μ3 = μ4 = μ5 = μ6 = μ7 = μ8 = μ9. C) H0: μ1 = μ2 = μ3 = μ4 = μ5. D) H0: μ1 = μ2 = μ3 = μ4 = μ5 = μ6 = μ7 = μ8 = μ9 = μ10.

C) H0: μ1 = μ2 = μ3 = μ4 = μ5.

The purpose of the randomized block design is to: A) distribute the differences between the groups equally. B) add an additional source of variation, improving upon the completely randomized design. C) control some of the extraneous sources of variation. D) isolate the treatment with the greatest effect.

C) control some of the extraneous sources of variation.

To determine whether the means of two populations are equal, _____. A) a chi-square test must be performed B) a t test must be performed C) either a t test or an analysis of variance can be performed D) an analysis of variance must be performed

C) either a t test or an analysis of variance can be performed

The mean square is the sum of squares divided by _____. A) the sample size B) the total number of observations C) its corresponding degrees of freedom D) its corresponding degrees of freedom minus 1

C) its corresponding degrees of freedom

The process of allocating the total sum of squares and degrees of freedom is called _____. A) replicating B) blocking C) partitioning D) factoring

C) partitioning

To test whether there is a difference between treatments A, B, and C, a sample of 12 observations have been randomly assigned to the 3 treatments. The results are given below. Treatment A - Observations : 20, 30, 25, 33 Treatment B- Observations: 22, 26, 20, 28 Treatment C- Observations: 40, 30, 28, 22 Determine the p-value. A) 0.04 B) 0.19 C) 0.08 D) 0.39

D) 0.39

In an analysis of variance problem, if SST = 120 and SSTR = 80, then SSE is _____. A) 120 B) 200 C) 80 D) 40

D) 40 120 = 80 + ____

What is the difference between a Complete block design and an incomplete block design? A) Complete block design indicates that every subject who has selected for the experiment agreed to participate. B) Complete block design indicates that all available subjects were utilized in the blocks. C) Complete block design indicates that the experiment was carried out to completion on every experimental unit. D) Complete block design indicates that each experimental unit of each block is subjected to all k treatments.

D) Complete block design indicates that each experimental unit of each block is subjected to all k treatments.

The effect produced when the levels of one factor interact with the levels of another factor in influencing the response variable is called: A) Factorial Design B) Replication C) Confounding D) Interaction

D) Interaction

The marketing department of a company has assigned three different boxes for its product. It wants to determine which box will produce the largest amount of sales. Each box will be test marketed in five different stores for a period of a month. The information on sales is given below. Box 1: Store 1 = 210, Store 2 = 230, Store 3 = 190, Store 4 = 180, Store 5 = 190 Box 2: Store 1 = 195, Store 2 = 170, Store 3 = 200, Store 4 = 190, Store 5 = 193 Box 3: Store 1 = 295, Store 2 = 275, Store 3 = 290, Store 4 = 275, Store 5 = 265 Identify the factors and the blocks. A) The factors are the box designs, and the blocks are the sales. B) The factors are the stores, and the blocks are the box designs. C) The factors are the sales, and the blocks are the box designs. D) The factors are the box designs, and the blocks are the stores.

D) The factors are the box designs, and the blocks are the stores.

An experimental design where the experimental units are randomly assigned to the treatments is known as _____. A) factor block design B) random factor design C) systematic sampling D) completely randomized design

D) completely randomized design

The objects of interest in the experiment are called the: A) response variables. B) treatments. C) experimental factors. D) experimental units.

D) experimental units.

A term that means the same as the term "variable" in an ANOVA procedure is _____. A) variance within B) treatment C) replication D) factor

D) factor

When carrying out an ANOVA from a randomized block design, which of the following options gives the degrees of freedom, respectively for the numerator and denominator of the test statistic? A) n - 1 and nT - k B) k - 1 and nT - k C) n - 1 and (k-1)(b-1) D) k - 1 and (k-1)(b-1)

D) k - 1 and (k-1)(b-1)

Statistical procedures that can be used to conduct statistical comparisons between pairs of population means are called: A) normal probability comparisons. B) ANOVA procedures. C) correlation analyses. D) multiple comparison procedures.

D) multiple comparison procedures.

The number of times each experimental condition is observed in a factorial design is known as a(n) _____. A) experimental condition B) partition C) factor D) replication

D) replication

The required condition for using an ANOVA procedure on data from several populations is that the _____. A) selected samples are dependent on each other B) sampled populations have equal means C) sampled populations are all uniform D) sampled populations have equal variances

D) sampled populations have equal variances

In the analysis of variance procedure (ANOVA), factor refers to _____. A) different levels of a treatment B) the dependent variable C) the critical value of F D) the independent variable

D) the independent variable

A local entrepreneur would like to know if those who live in a rural community are more likely to buy a real Christmas tree than those who live in an urban community. He takes a random sample of 100 people who reside in the city and a separate random sample of 100 people who live in the country and asks them if they buy a real tree at Christmas time. Of the urban participants, 22 buy a real tree. Of the rural participants, 28 buy a real tree. Let p1 = the proportion of all people who live in rural communities that buy a real Christmas tree and let p2 = the proportion of all people who live in urban communities that buy a real Christmas tree. State the null and alternative hypothesis.

H0 : p1 - p2 ≤ 0, Ha : p1 - p2 > 0

A fast food restaurant has automatic drink dispensers to help fill orders more quickly. When the 12 ounce button is pressed, they would like for exactly 12 ounces of beverage to be dispensed. There is, however, undoubtedly some variation in this amount. The company does not want the machine to systematically over fill or under fill the cups. Which of the following gives the correct set of hypotheses?

H0 : u = 12 Ha : u not = 12

It has been stated that at least 75 out of every 100 people who go to the movies on Saturday night buy popcorn. Identify the null and alternative hypothesis.

H0: p ≥ 0.75, Hα: p < 0.75

A student wants to determine if pennies are really fair, meaning equally likely to land heads up or tails up. He flips a random sample of 50 pennies and finds that 28 of them land heads up. What are the appropriate null and alternative hypotheses?

H0: p= 0.5, Hα: p ≠ 0.5

The average gasoline price of one of the major oil companies has been hovering around $2.20 per gallon. Because of cost reduction measures, it is announced that there will be a significant reduction in the average price over the next month. In order to test this belief, we wait one month, then randomly select a sample of 36 of the company's gas stations. We find that the average price for the stations in the sample was $2.15. The standard deviation of the prices for the selected gas stations is $0.10. State the appropriate null and alternative hypothesis for testing the company's claim.

Ho : u >= $2.20 Ha : u < $2.20

A news reporter states that the average number of temperature in January has never dropped below 10 degrees Fahrenheit. You go online to research this claim. The appropriate hypotheses are

Ho : u >= 10 Ha : u < 10

The average number of hours for a random sample of mail order pharmacists from company A was 50.1 hours last year. It is believed that changes to medical insurance have led to a reduction in the average work week. To test the validity of this belief, the hypotheses are

Ho : u >= 50.1 Ha : u < 50.1

An elementary school teacher asked a random sample of 12 of her students what their favorite number was. Assume the population of responses would follow a normal distribution. The students stated that their favorite numbers are: 2 10 7 4 0 5 6 4 4 6 1 100 Suppose we were to create a 95% confidence interval for μ. What effect does the value 100 have on the width of the confidence interval?

It makes the interval wider.

confidence coefficient

The confidence level expressed as a decimal value. For example, .95 is the confidence coefficient for a 95% confidence level.

The independent variable is the advertising expenses, and the dependent variable is sales.

σ unknown

The more common case when no good basis exists for estimating the population standard deviation prior to taking the sample. The interval estimation procedure uses the sample standard deviation s in computing the margin of error.

Following is a portion of the computer output for a regression analysis relating y = number of people who use the public pool to x = the outside temperature. Predictor Coef Stdev t-ratio P Constant. 57.912 5.674 10.21 0.000 Temp 0.81138 0.09038 8.98 0.000 s=1.198 R-sq=94.2% R-sq(adj)=93% Test for a significant relationship between the number of people who use the public pool and the outside temperature. Use ⍺ =.05. State your conclusion.

The p-value < .05. The data provide evidence of a significant relationship between the number of people who use the public pool and the outside temperature.

The average gasoline price of one of the major oil companies has been hovering around $2.20 per gallon. Because of cost reduction measures, it is announced that there will be a significant reduction in the average price over the next month. In order to test this belief, we wait one month, then randomly select a sample of 36 of the company's gas stations. We find that the average price for the stations in the sample was $2.15. The standard deviation of the prices for the selected gas stations is $0.10. Given that the p-value is 0.002, state the conclusion. Use α = 0.01.

The p-value is less than α = 0.01, so we can reject H0.

Level of significance

The probability that the interval estimation procedure will generate an interval that does not contain μ.

The following data represent a company's yearly sales volume and its advertising expenditure over a period of 8 years. Advertising Expenses: 32, 33, 35, 34, 36, 37, 39, 42 Sales: 15, 16, 18, 17, 16, 19, 19, 24 Create a scatter diagram in order to answer the following question: What does the scatter diagram indicate about the relationship between the two variables?

The scatter diagram indicates a positive relationship between advertising expenses and sales.

A doctor would like to know if men and women got the same amount of sleep per night or if women tended to get less sleep than men. He took a random sample of 100 of his male and 100 of his female patients and asked them how many hours of sleep they got, per night, on average. The women slept an average of 6.75 hours and the men slept an average of 7.5 hours. Suppose we also knew the population standard deviations to be 1.25 hours and 1.5 hours for men and women, respectively. Based on the sample data, can you conclude that the women get less sleep than men do, on average?

Yes! The p-value is less than α = 0.05, so the sample results do provide sufficient evidence to conclude women sleep less than men do, on average.

A local entrepreneur would like to know if those who live in an urban or rural community are more likely to buy a real Christmas tree. He takes a random sample of 100 people who reside in the city and a separate random sample of 100 people who live in the country and asks them if they buy a real tree at Christmas time. Of the urban participants, 22 buy a real tree. Of the rural participants, 28 buy a real tree. Based upon this data, can we assume a normal distribution?

Yes, n1p1 = 22 n1(1-p1) = 78 n12p2 = 28 n12(1-p2) = 72 Which are all greater than 5

Which of the following scenarios follows a matched sample design?

a teacher uses a retest and then a posttest with her students to see how much they have improved

A sample of 21 observations yielded a sample variance of 16. If we want to test H₀: σ² = 16, the test statistic is a.20. b.21. c.5. d.50.

a.20. χ² = (n-1)(s²)/𝜎² = (21-1)(16)/(16) = 20

What is the probability of obtaining a χ² value such that χ²₀.₉ ≤ χ² ≤ χ²₀.₁? a.80% b.90% c.95% d.99%

a.80%

The standard deviation of the ages of a sample of 16 executives from City A, on the east coast was 5.2 years; while the standard deviation of the ages of a sample of 21 executives from City B on the west coast was 12.8 years. State the appropriate null and alternative hypotheses that can be used to determine if there is a difference in the population variances of the ages of all the east coast and west coast executives. a.H₀ : σ₁ = σ₂, Ha : σ₁ ≠ σ₂ b.H₀ : σ₁ ≥ σ₂, Ha : σ₁ < σ₂ c.H₀ : σ₁ ≤ σ₂, Ha : σ₁ > σ₂ d.H₀ : s₁ = s₂, Ha : s₁ ≠ s₂

a.H₀ : σ₁ = σ₂, Ha : σ₁ ≠ σ₂

Based on the sample evidence below, we want to test the hypothesis that population A has a larger variance than population B. Sample A Sample B s² 12.1 5 n 11 10 Does this data provide convincing evidence that population A has a larger variance than population B? Determine the p-value and state the conclusion. a.The p-value is greater than 0.1. The data do not provide convincing evidence that population A has a larger variance than population B. b.The p-value is between 0.05 and 0.1. The data do not provide convincing evidence that population A has a larger variance than population B. c.The p-value is between 0.01 and 0.05. The data provide convincing evidence that population A has a larger variance than population B. d.The p-value is less than 0.01. The data provide convincing evidence that population A has a larger variance than population B.

a.The p-value is greater than 0.1. The data do not provide convincing evidence that population A has a larger variance than population B. We must use an F distribution with 10 degrees of freedom in the numerator and 9 degrees of freedom in the denominator to look up the test statistic of 2.42. The p-value is greater than 0.1.

An egg packing company has stated that the standard deviation of the weights of their grade A large eggs is 0.07 ounces or less. The sample variance for 51 eggs was 0.0065 ounces. Can this sample result confirm the company's claim? Use α = 0.01. a.The p-value is less than α = 0.01, so the data support the belief that the standard deviation of the weights of the grade A large eggs is greater than 0.07 ounces. b.The p-value is greater than α = 0.01, so the data support the belief that the standard deviation of the weights of the grade A large eggs is greater than 0.07 ounces. c.The p-value is less than α = 0.01, so the data do not support the belief that the standard deviation of the weights of the grade A large eggs is greater than 0.07 ounces. d.The p-value is greater than α = 0.01, so the data do not support the belief that the standard deviation of the weights of the grade A large eggs is greater than 0.07 ounces.

a.The p-value is less than α = 0.01, so the data support the belief that the standard deviation of the weights of the grade A large eggs is greater than 0.07 ounces.

When testing for the equality of two population variances, the population which yielded the larger sample variance should always be referred to as a.population 1. b.population 2. c.the standard population. d.the basis of comparison.

a.population 1.

confidence interval

another name for an interval estimate

When working with regression analysis, an outlier is:

any observation that does not fit the trend shown by the remaining data.

Suppose a residual plot of x verses the residuals, y - ŷ, shows a nonconstant variance. In particular, as the values of x increase, suppose that the values of the residuals also increase. This means that:

as the values of x get larger, the ability to predict y becomes less accurate. If, as the values of x increase, the values of the residuals also increase we can conclude that as the values of x get larger, the ability to predict y becomes less accurate.

For a lower tail test, the p-value is the probability of obtaining a value for the test statistic

at least as small as that provided by the sample

A machine produces pipes used in airplanes. The average length of the pipe is 16 inches. The acceptable variance for the length is 0.3 inches. A sample of 25 pipes was taken. The average length in the sample was 15.95 inches with a standard deviation of 0.4 inches. Which of the following gives the 95% confidence interval estimate of the population variance? a. (24)(0.3²)/39.364 ≤ 𝜎² ≤ (24)(0.3²)/12.401 b. (24)(0.4²)/39.364 ≤ 𝜎² ≤ (24)(0.4²)/12.401 c. (24)(0.3)/39.364 ≤ 𝜎² ≤ (24)(0.3)/12.401 d. (24)(0.4)/39.364 ≤ 𝜎² ≤ (24)(0.4)/12.401

b. (24)(0.4²)/39.364 ≤ 𝜎² ≤ (24)(0.4²)/12.401 This is based upon a sample size of 25, sample standard deviation of 0.4 and chi-square critical values based on 24 degrees of freedom with a probability of 0.025 and 0.975 to the right.

A machine produces pipes used in airplanes. The average length of the pipe is 16 inches. The acceptable variance for the length is 0.3 inches. A sample of 25 pipes was taken. The average length in the sample was 15.95 inches with a standard deviation of 0.4 inches. Which of the following gives the 95% confidence interval estimate of the population standard deviation? a. √(24)(0.3²)/39.364 ≤ 𝜎 ≤ √(24)(0.3²)/12.401 b. √(24)(0.4²)/39.364 ≤ 𝜎 ≤ √(24)(0.4²)/12.401 c. (24)(0.3)/39.364 ≤ 𝜎 ≤ (24)(0.3)/12.401 d. (24)(0.4)/39.364 ≤ 𝜎 ≤ (24)(0.4)/12.401

b. √(24)(0.4²)/39.364 ≤ 𝜎 ≤ √(24)(0.4²)/12.401

The value of F₀.₀₅ with 20 numerator and 10 denominator degrees of freedom is a.2.35. b.2.77. c.3.37. d.3.42.

b.2.77. (Use numerator/denominator table)

The chi-square value for a one-tailed (upper tail) hypothesis test at 95% confidence with a sample size of 25 is a.33.20. b.36.42. c.39.36. d.37.65.

b.36.42. (Use a Chi-Square table at the intersection of 24 degrees of freedom and an upper tail probability of 0.05)

What percent of the sampling distribution lies above F₀.₀₅ with 9 degrees of freedom in the numerator and 14 degrees of freedom in the denominator? a.2.5% b.5% c.10% d.Cannot be determined from the information provided.

b.5% (The degrees of freedom information is irrelevant)

Which of the following statements is true? a.The values of the F statistic range from -∞ to ∞. b.An F test statistic must always be a positive number. c.The F distribution is always strongly skewed left. d.The F distribution can only be used for one-sided hypothesis tests.

b.An F test statistic must always be a positive number.

Based on the sample evidence below, we want to test the hypothesis that population A has a larger variance than population B. Sample A Sample B s² 12.1 5 n 11 10 State the appropriate null and alternative hypothesis. a.H₀ : σ₁ ≥ σ₂, Ha : σ₁ < σ₂ b.H₀ : σ₁ ≤ σ₂, Ha : σ₁ > σ₂ c.H₀ : s₁ ≥ s₂, Ha : s₁ > s₂ d.H₀ : s₁ ≤ s₂, Ha : s₁ < s₂

b.H₀ : σ₁ ≤ σ₂, Ha : σ₁ > σ₂

Based on the sample evidence below, we want to test the hypothesis that population A has a larger variance than population B. Sample A Sample B s² 12.1 5 n 11 10 What are the degrees of freedom for the test statistic? a.There are 9 degrees of freedom in the numerator and 10 degrees of freedom in the denominator. b.There are 10 degrees of freedom in the numerator and 9 degrees of freedom in the denominator. c.There are 11 degrees of freedom in the numerator and 10 degrees of freedom in the denominator. d.There are 20 degrees of freedom in the numerator and 20 degrees of freedom in the denominator.

b.There are 10 degrees of freedom in the numerator and 9 degrees of freedom in the denominator.

A one-tailed hypothesis test about two population variances will always be formulated as a.a lower tail test. b.an upper tail test. c.a two-sided test. d.a multi-sided test.

b.an upper tail test.

A sample of n observations is taken from a population. The appropriate chi-square distribution has a.n degrees of freedom. b.n - 1 degrees of freedom. c.n - 2 degrees of freedom. d.n - 3 degrees of freedom.

b.n - 1 degrees of freedom.

An F distribution has a.a left skewed distribution. b.n₁ - 1 degrees of freedom in the numerator and n₂ - 1 degrees of freedom in the denominator. c.values that range from -∞ to ∞. d.a uniform distribution.

b.n₁ - 1 degrees of freedom in the numerator and n₂ - 1 degrees of freedom in the denominator.

The F distribution is a family of curves that are a.approximately normal. b.skewed to the right. c.skewed to the left. d.fairly symmetric.

b.skewed to the right.

The symbol used for the variance of the population is a.σ. b.σ². c.s. d.s².

b.σ².

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution:

becomes smaller

As the test statistic becomes larger, the p-value

becomes smaller

When the level of confidence decreases, the margin of error:

becomes smaller

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

can be approximated by a normal distribution

If the coefficient of determination is a positive value, then the coefficient of correlation:

can be either positive or negative

The value of the coefficient of correlation (r):

can be equal to the value of the coefficient of determination (r^2)

The coefficient of determination:

cannot by negative

A machine produces pipes used in airplanes. The average length of the pipe is 16 inches. The acceptable variance for the length is 0.3 inches. A sample of 25 pipes was taken. The average length in the sample was 15.95 inches with a variance of 0.4 inches. Which of the following gives the 95% confidence interval estimate of the population variance? a. (24)(0.3²)/39.364 ≤ 𝜎² ≤ (24)(0.3²)/12.401 b. (24)(0.4²)/39.364 ≤ 𝜎² ≤ (24)(0.4²)/12.401 c. (24)(0.3)/39.364 ≤ 𝜎² ≤ (24)(0.3)/12.401 d. (24)(0.4)/39.364 ≤ 𝜎² ≤ (24)(0.4)/12.401

d. (24)(0.4)/39.364 ≤ 𝜎² ≤ (24)(0.4)/12.401

We are interested in testing whether the variance of a population is significantly less than 4. The null hypothesis for this test is a. H₀: 𝜎² < 4 b. H₀: s² ≥ 4 c. H₀: 𝜎 < 2 d. H₀: 𝜎² ≥ 4

d. H₀: 𝜎² ≥ 4

An egg packing company has stated that the standard deviation of the weights of their grade A large eggs is 0.07 ounces or less. The sample variance for 51 eggs was 0.0065 ounces. Can this sample result confirm the company's claim? The test statistic is χ² = 0.43. Find the p-value. a.The p-value is less than 0.01. b.The p-value is between 0.01 and 0.05. c.The p-value is between 0.05 and 0.25. d.The p-value is greater than 0.25.

d.The p-value is greater than 0.25. Based upon a chi-square distribution with 50 degrees of freedom, the p-value is greater than 0.25

The standard deviation of the ages of a sample of 16 executives from City A, on the east coast was 5.2 years; while the standard deviation of the ages of a sample of 21 executives from City B on the west coast was 12.8 years. At α = 0.05, test to see if there is any difference in the population variances of the ages of all the east coast and west coast executives. a.The p-value is greater than 0.1. The data do not provide convincing evidence that there is a difference in the population variances of the ages of all the east and west coast executives. b.The p-value is between 0.05 and 0.1. The data do not provide convincing evidence that there is a difference in the population variances of the ages of all the east and west coast executives. c.The p-value is between 0.02 and 0.10. The data do not provide convincing evidence that there is a difference in the population variances of the ages of all the east and west coast executives. d.The p-value is less than 0.02. The data do not provide convincing evidence that there is a difference in the population variances of the ages of all the east and west coast executives.

d.The p-value is less than 0.02. The data do not provide convincing evidence that there is a difference in the population variances of the ages of all the east and west coast executives.

Whenever the variances of two normal populations are equal the sampling distribution of the ratio of the two sample variances has a.a normal distribution with a mean of 0 and a standard deviation of 1. b.a chi-squared distribution with k - 1 degrees of freedom. c.a binomial distribution with parameters n and p. d.an F distribution with n₁ - 1 degrees of freedom in the numerator and n₂ - 1 degrees of freedom in the denominator.

d.an F distribution with n₁ - 1 degrees of freedom in the numerator and n₂ - 1 degrees of freedom in the denominator.

The random variable for a chi-square distribution may assume a.any value between -1 to 1. b.any value between -infinity to infinity. c.any negative value. d.any value greater than zero.

d.any value greater than zero.

For an F distribution, the number of degrees of freedom for the numerator a.must be larger than the number of degrees for the denominator. b.must be smaller than the number of degrees of freedom for the denominator. c.must be equal to the number of degrees of freedom for the denominator. d.can be larger, smaller, or equal to the number of degrees of freedom for the denominator.

d.can be larger, smaller, or equal to the number of degrees of freedom for the denominator.

The symbol used for the variance of the sample is a.σ. b.σ². c.s. d.s².

d.s².

As the sample size increases, the margin of error:

decreases

In regression analysis, the variable that is being predicted is the:

dependent variable

Larger values of r^2 imply that the observations are more closely grouped about the:

least squares line

The probability of making a Type I error when the null hypothesis is true as an equality is called the

level of significance

The probability that the interval estimation procedure will generate an interval that does not contain µ is known as the:

level of significance.

A company wants to identify which of two production methods has the smaller 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

The p-value

must be a number between 0 and 1

For a fixed sample size, n, in order to have a higher degree of confidence, the margin of error and the width of the interval:

must be larger

A poll of 600 voters showed 210 that were in favor of stricter gun control measures. Develop a 90% confidence interval estimate for the proportion of all the voters who are in favor of stricter gun control measures.

n 600 210 point estimate 0.3500 tα/2 1.64 margin of error 0.0319 Lower 0.32 Upper 0.38

For the case where σ is unknown, the test statistic has a t distribution. How many degrees of freedom does it have?

n-1

For a fixed confidence level and population standard deviation, if we would like to cut our margin of error to 1/3 of the original size, we should take a sample size that is:

nine times as large as the original sample size.

Influential observations always: a. increase the value of the slope. b. increase the value of the correlation. c. increase the value of the y-intercept. d. none of the above are correct

none of the above are correct Influential observations can increase or decrease the value of the slope, correlation, and y-intercept depending on where they fall in relation to the rest of the points in the data set.

The tests of significance in regression analysis are based on assumptions about the error term ɛ. One such assumption is that the error term follows ɛ a(n) _____ distribution for all values of x.

normal

The sampling distribution of p̅1 - p̅2 is approximated by a

normal distribution

A graph of the standardized residuals plotted against values of the normal scores that helps to determine whether the assumption that the error term has a normal probability distribution appears to be valid is called a:

normal probability plot

The normal probability distribution can be used to approximate the sampling distribution of p as long as

np ≥ 5 and n(1 − p) ≥ 5

The sampling distribution of can be approximated by a normal distribution as long as:

np>5 and n(1-p)>5

The p-value is a probability that measures the support (or lack of support) for the

null hypothesis

A student wants to determine if pennies are really fair, meaning equally likely to land heads up or tails up. He flips a random sample of 50 pennies and finds that 28 of them land heads up. Calculate the p-value and state the conclusion. Use α = 0.05.

p-value = 0.396. Do not reject H0

When completing a two-tailed hypothesis test about the difference between two population means the

p-value must be doubled

When studying the relationship between two quantitative variables, whenever we want to predict an individual value of y for a new observation corresponding to a given value of x, we should use a(n):

prediction interval

The mathematical equation relating the independent variable to the expected value of the dependent variable, E(y) = B0 + B1x , is known as the:

regression equation

In regression analysis, the equation in the form y = 𝛽0 + 𝛽1x + ε is called the:

regression model

t = (1.5 - 0 ) / (1.414 / (sq root 8))

The following data show the results of an aptitude test and the grade point average of 10 students. GPA: 1.8, 2.3, 2.6, 2.4, 2.8, 3.0, 3.4, 3.2, 3.6, 3.8 Aptitude Test Scores: 26, 31, 28, 30, 34, 38, 41, 44, 40, 43 Does the t test indicate a significant relationship between GPA and Aptitude Test Score? State the test statistic, and then state your conclusion using ⍺ = .05.

t = 6.25. The p- value is less than .05, so the evidence is sufficient to conclude that a significant relationship exists between GPA and Aptitude Test Scores. t = b1 / sb1 b1 = sum of (xi -xbar)(yi - ybar) / (xi - xbar)^2 sb1 = s / sqrt of sum of (xi - xbar)^2 s = sqrt of MSE t = 6.25 Find P val Go to t table, df = 8, find t of 6.25. 6.25 is not on the t table so its less than 0.05

When "s" is used to estimate "σ," the margin of error is computed by using the:

t distribution

When constructing a confidence or a prediction interval to quantify the relationship between two quantitative variables, what distribution do confidence and prediction intervals follow?

t distribution Confidence and prediction intervals follow a t distribution.

From a population that is normally distributed, a sample of 30 elements is selected and the standard deviation of the sample is computed. For the interval estimation of μ, the proper distribution to use is the:

t distribution with 29 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

t distribution with 70 degrees of freedom

t test for a difference in two means

t= 2.15 - 2.20 / (.10 / Sq root of 36)

In most applications of the interval estimation and hypothesis testing procedures, random samples with n1 ≥ 30 and n2 ≥ 30 are adequate. In cases where either or both sample sizes are less than 30

the distribution of the populations becomes an important consideration

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

the level of significance

For the interval estimation of μ when σ is known and the sample is large, the proper distribution to use is:

the normal distribution.

In hypothesis testing, the tentative assumption about the population parameter is called

the null hypothesis

If a residual plot of x versus the residuals, y - ŷ, shows a non-linear pattern, then we should conclude that:

the regression model is not an adequate representation of the relationship between the variables.

To compute the necessary sample size for an interval estimate of a population proportion, all of the following procedures are recommended when p* is unknown except:

using .95 as an estimate.

To compute the necessary sample size for an interval estimate of a population mean, all of the following procedures are recommended when σ is unknown except:

using σ = 1

A doctor would like to know if men and women got the same amount of sleep per night or if women tended to get less sleep than men. He took a random sample of 100 of his male and 100 of his female patients and asked them how many hours of sleep they got, per night, on average. The women slept an average of 6.75 hours and the men slept an average of 7.5 hours. Suppose we also knew the population standard deviations to be 1.25 hours and 1.5 hours for men and women, respectively. Which of the following correctly gives the test statistic?

z = (7.5 - 6.75) / Sq root of ((1.5^2 / 100) + (1.25^2 / 100))

A student believes that no more than 20% of the students who finish a statistics course get an A. A random sample of 100 students was taken. Twenty-two percent of the students in the sample received A's. Calculate the test statistic.

qmb 3200 exam 3 ch14, ST 560 Module 11, Chapter 13 Quiz, Chapter 8: Interval Estimation, Stat chapter 10, stat exam 3 (ch. 9)

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