# statistics The data in the file spending represent the per-capita spending

6.14 Show that for a sample of n = 39, the smallest and largest Z values are – 1.96 and + 1.96, and the middle (i.e., 20th) Z value is 0.00.

6.19 The data in the file spending represent the per-capita spending, in thousands of dollars, for each state in 2004. Decide whether the data appear to be approximately normally distributed by

A. Comparing data characteristics to theoretical properties.

B. Constructing a normal probability plot.

7.1. For a population containing N=902 individuals what code number would you assign for

(a)The first person on the list?

(b) The fortieth person on the list?

© The last person on the list?

.7.8.Prenumbered sales invoices are kept in a sales journal.The invoices are numbered from 0001 to 5000.

(a)beginning in row 16,column 1,and proceeding horizontally in Table E.1,select a sample of 50 invoice numbers.

(b)select a systematic sample of 50 invoice numbers.Use the random numbers in row 20,columns 5-7 ,as the starting point for your selection.

©Are the invoices selected in (a) the same as those selected in(b)?why or why not?

7.21. The diameter of a brand of ping-pong ball is approximately normally distributed, with a mean of 1.30 inches and a standard deviation of 0.04 inch. If you select a random sample of 16 ping-pong balls,

(a) What is the sampling distribution of the mean?

(b) What is the probability that the sample mean is less than 1.28 inches?

©what is the probability that the sample mean is between 1.31 and1.33 inches?

(d) The probability is 60% that the sample mean is between will be between what two values, symmetrically distributed around the population mean?

7.27. In a random sample of 64 people, 48 are classified as “successful.”

(a) Dete

rmine the sample proportion, P, of “successful” people.

(b)If the population proportion is 0.07, determine the standard error of the proportion.

8.1. If X = 85, mean=8, n=64, construct a 95% confidence interval estimate of the population mean, U.

8.2. If X = 125, mean = 24, and n = 36, construct a 99% confidence interval estimate of the population mean, U.

8.3. A market researcher collects a simple random sample of n = 100 customers from its population of two million customers. After analyzing the sample, she states that she has 95% confidence that the mean annual income of its two million customers is between $70,000 and $85,000.

Explain the meaning of this statement.

8.8. Determine the critical value of t in each of the following circumstances:

A. 1 – a = 0.95, n = 10

B. 1 – a = 0.99, n=10

C. 1 – a = 0.95, n=32

D. 1 – a = 0.95, n = 65

E. 1 – a = 0.90, n=16

8.16. The data in the file SUV represents the overall miles per gallon (MPG) of 2007 small SUVs.

Model MPG Model MPG

Toyota RAV 4 6-cyl 22 Mazda Tribute 18

Hyundai Santa Fe 18 Mercury 18

Toyota RAV 4 4-cyl 23 Mariner Luxury

Subaru Forester 20 Nissan Xterra 17

Sports 2.5 XT Honda Element 21

Honda CR- V 21 Suzuki Grand Vitara 18

Subaru Forester 22 Chevrolet Equinox 18

8.27. In a start of the twenty-first century saw many corporate scandals and many individuals lost faith in business.In a 2007 poll conducted by new York city-based Edelman public relations firm,57% of respondents say they trust business to “do what is right.”This percentage was the highest in the annual survey since 2001

(a) construct a 95% confidence interval estimate of the population proportion of individuals who trust the business to”do what is right”assuming that the poll surveyed:

1.100 individuals.

2.200 individuals.

3.300 individuals.

(b) Discuss the effect that sample size on the width of confidence intervals.

(c)Interprete the interval in (a)

8.32.If you want to be 95% confident of estimating the population mean to within a sampling error of +/_5 and the standard deviation is measured to be 15,what sample size is required?

8.44.In 2005,34% of workers reported that their jobs were more difficult,with more stress,and 37% reported that they worry about retiring comfortably.consider a follow-up study to be conducted in the near future.

(a)What sample size is needed to estimate the population proportion of workers who reported that their jobs were more stress,to within +/- 0.02 with 95% confidence?

(b)How many workers need to be sampled in order to estimate the population proportion of workers who worried about retiring comfortably to within +/- 0.02 with 95% confidence?

(c )compare the results of(a) and (b).Explain why these results differ.

(d)If you were to design the follow-up study,would you use one sample and ask the respondents both questions,or would you select two separate samples?Explain the rationale behind your decision.

9.1.For Ho:u=100,H1:u not equal 100,and for a sample of size n,why beta larger if the actual value of u(mean)is 90 than if the actual value of u is 75?

9.2.If you use a 0.05 level of significance in a(two-tail)hypothesis test,what will you decide if Zstat=+2.21?

9.3.If you use a 0.01 level of significance in a(two-tail)hypothesis test,what is your decision rule for rejecting a null hypothesis that the population mean is 500 if you see the Z test?

9.11.The U.S.Food and Drug Administration(FDA) is responsible for approving new drugs.Many consumer groups feel that the approval process is too easy and,therefore,too many drugs are approved that are later found to be unsafe.On the other hand,a number of industry lobbyist are pushing for a more lenient approval process so that pharmaceutical companies can get new drugs approved more easily and quickly.consider a null hypothesis that a new,unapproved drug is unsafe and an alternative hypothesis that a new,unapproved drug is safe.

(a)Explain the risks of committing a type I or Type II error.

(b)which type of error are the consumer groups trying to avoid?Explain.

(c )which type of error are the industry lobbyists trying to avoid?Explain.

(d)how would it be possible to lower the chances of both Type I and Type II errors?

9.16.if,in a sample of n=16 selected from a normal population,X bar=56 and S=12,what is the value of t STAT if you are testing the null hypothesis Ho:mean=50?

9.22.Late payment of medical claims can add to the cost of health care.An article reported that the mean time from the date of service to the date of payment for one insurance company was 41.4 days during a recent period.Suppose that a sample of 100 medical claims is selected during the latest time period.The sample mean time from the date of service to the date of payment was 39.6 days,and the sample standard deviation was 7.4 days.

(a)Using the 0.05 level of significance,is there evidence that the population mean has changed from 41.4 days?

(b)What is your answer in(a)if you use the 0.01 level of significance?

(c )What is your answer in(a)if the sample mean is 38.2 days and the sample standard deviation is 10.7 days?

(d)Because the sample size is 100,do you need to be concerned about the shape of the population distribution when conducting the t-test in( a)?Explain.

9.34. In a one-tail hypothesis test where you reject Ho only in the upper tail,what is the P-value if Z=stat=+2.00?

9.45.You are the manager of a restaurant that delivers pizza to collect dormitory rooms. You have just changed your delivery process in an effort to reduce the mean time between the order and completion of delivery from the current 25 minutes.A sample of 36 orders using the new delivery process yields a sample mean of 22.4 minutes and a sample standard deviation of 6 minutes.

(a)Using the six-step critical value approach,at the 0.05 level of significance,is there evidence that the population mean delivery time has been reduced below the previous populatation mean value of 25 minutes?

(b)At the 0.05 level of significance,use the five-step P-value approach.

(c )Interpret the meaning of the P-value in(b).

(d)Compare your conclusions in(a)and(b).

9.48.If,in a random sample of 400 items,88 are defective,what is the sample proportion of defective items?

9.51.Late payment of medical claims can add to the cost of health care.An article reported that for one insurance company,85.1% of the claims were paid in full when first submitted.Suppose that the insurance company developed a new payment system in an effort to increase this percentage.A sample of 200 claims processed under this system revealed that 180 of the claims were paid in full when first submitted.

(a)At the 0.05 level of significance,is there evidence that the population proportion of claims processed under this new system is higher than the article reported for the previous system?

(b)Compute the P-value and interpret its meaning.

9.57.A coin-operated soft-drink machine is designed to discharged on average,at least 7 ounces of beverages per cup with a standard deviation of 0.2 ounce.The amount of beverage per cup is normally distributed.If you select a random sample of 16 cups and you are willing to have an alpha=0.05 risk of committing a Type I error,compute the power of the test and the probability of a Type II error(beta)if the population mean amount dispensed is actually

(a) 6.9 ounces per cup.

(b) 6.8 ounces per cup.

10.1.If you have samples of n1=12 and n2=15,in performing the pooled-variance t test,how many degrees of freedom do you have?

10.2.Assume that you have a sample of n1=8,with the sample mean Xbar1=42,and a sample standard deviation of S1=4,and you have an independent sample of n2=15 from another population with a sample mean of Xbar2=34 and the sample standard deviation S2=5.

(a)what is the value of the pooled-variance t STAT test statistics for testing H0:Mean1=mean2?

(b)In finding the critical value t alpha/2,how many degrees of freedom are there?

( c)Using the level of significance beta=0.01,what is the critical value for a one-tail test of the hypothesis Ho:mean1greater than mean 2?

(d)what is your statistical decision?

10.10.When do children in the united states develop preference for brand name products?In a study reported,marketers showed children identical pictures of athletics shoes.one picture was labeled Nike,and one was labeled K-Mart.The children were asked to evaluate the shoes based on their appearance,quality,price,prestige,favorableness,and preference for owning.A score from 2 to -2 was recorded for each child.The following table reports the results of the study:

Age by Brand Sample size Sample Mean Sample Standard Deviation

Age 8

Nike 27 0.89 0.98

K-Mart 22 0.86 1.07

Age 12

Nike 39 0.88 1.01

K-Mart 41 0.09 1.08

Age 16

Nike 35 0.41 0.81

K-Mart 33 -0.29 0.92

(a)Conduct a pooled-variance t test for the difference between the two means for each of the three age groups.Use a level of significance of 0.05.

(b)What assumptions are needed to conduct the tests in(a)?

(c )Write a brief summary of your findings.

10.20.An experimental design for a paired t test has 20 pairs of identical twins.How many degrees of freedom are in this t test?

10.22.Nine experts rated two brands of Colombian coffee in a taste-testing experiment.A rating on a 7- point scale(1=extremely unpleasing,7=extremely pleasing)is giving for each of four characteristics:taste,aroma,richness,and acidity.The following data displays the summated ratings-accumulated over all four characteristics.

EXPERT BRAND

A B

C.C. 24 26

S.E. 27 27

E.G. 19 22

B.L. 24 27

C.M. 22 25

C.N. 26 27

G.N. 27 26

R.M. 25 27

P.V. 22 23

(a.) At the 0.05 level of significance, is there evidence of a difference in the mean summated ratings between the two brand?

(b.) What assumption is necessary about the population distribution in order to perform this test?

(c.) Determine the p-value in (a) and interpret its meaning.

(d.) Construct and interpret a 95% confidence interval estimate of the difference in the mean summated ratings between the two brands.

10.29 Let n1 = 100, X1 = 50, n2 = 100, and X2 =30.

a. At the 0.05 level of significance, is there evidence of a significant difference between the two population proportions?

b. Construct a 95% confidence interval estimate of the difference between the two population proportions?

10.31 A sample of 500 shoppers was selected in a large metropolitan area to determine various information concerning consumer behavior. Among the questions asked was, “Do you enjoy shopping for clothing?” Of 240 males, 136 answered yes. Of 260 females, 224 answered yes.

a. Is there evidence of a significant difference between males and females in the proportion that enjoy shopping for clothing at the 0.01 level of significance?

b. Find the p-value in (a) and interpret its meaning.

c. Construct and interpret a 99% confidence interval estimate of the difference between the proportion of males and females who enjoy shopping for clothing?

11.1. An experiment has a single factor with five groups and seven values in each group.

a. How many degrees of freedom are there in determining the among-group variation?

b. How many degrees of freedom are there in determining the within-group variation?

c. How many degrees of freedom are there in determining the total variation?

11.2 You are working with the same experiment as in problem 11.1.

a. If SSA = 60 and SST = 210, what is SSW?

b. What is MSA?

c. What is MSW?

d. What is the value of F stat?

11.7 The computer Anxiety Rating Scale (CARS) measures an individual’s level of computer anxiety, on a scale from 20 (no anxiety) to 100 (highest level of anxiety).Researchers at Miami University administered CARS to 172 business students. One of the objectives of the study was to determine whether there are differences in the amount of computer anxiety experienced by students with different majors. They found the following:

Source Degrees of Freedom Sum of Squares Mean Squares F

Among 5 3,172

majors

Within 166 21,246

majors

Total 171 24,418 Major n Mean Marketing 19 44.37

Management 11 43.18

Other 14 42.21

Finance 45 41.80

Accountancy 36 37.56

MIS 47 32.21

a. Complete the ANOVA summary table

b. At the 0.05 level of significance, is there evidence of a difference in the mean computer anxiety experienced by different majors?

c. If the results in (b) indicate that it is appropriate, use the Turkey-Kramer procedure to determine which majors differ in mean computer anxiety. Discuss your findings.

12.1. Determine the critical value of Xsquare with 1 degree of freedom in each of the following circumstances:

a. a = 0.01

b. a = 0.025

c. a = 0.05

12.3 Use the following contingency table:

A B Total

1 20 30 50

2 30 45 75

Total 50 75 125

a. Find the expected frequency for each cell.

b. Compare the observed and expected frequencies for each cell

c. Compute Xsquare STAT. Is it significant at a = 0.05?

12.5 A sample of 500 shoppers was selected in a large metropolitan area to determine various information concerning consumer behavior. Among the questions asked was, “Do you enjoy shopping for clothing?” The results are summarized in the following contingency table:

ENJOY SHOPPING GENDER

FOR CLOTHING Male Female Total

Yes 136 224 360

No 104 36 140

Total 240 260 500

(a)Is there evidence of a significant difference between the proportion of males and females who enjoy shopping for clothing at the 0.01 level of significance?

(b)Determining the P-value in(a) and interpret its meaning.

( c)What are your answers to(a) and(b)if 206 males enjoyed shopping for clothing and 34 did not?

(d)Compare the results of (a)through(c)to those of problem 10.31(a)through(c) .

12.11.Consider a contingency table with two rows and five columns.

(a)Find the degree of freedom.

(b)Find the critical value for alpha=0.05.

(c) Find the critical value for alpha=0.01

12.12.Use the following contingency table:

A B C TOTAL

1 10 30 50 90

2 40 45 50 135

Total 50 75 100 225

(a)Compute the expected frequencies for each cell.

(b)Compute XsquareSTAT.Is it significant at alpha=0.05?

( c)If appropriate,use the Marascuilo procedure and alpha=0.05 to determine which groups are determine which groups are different.

12.14.A survey was conducted in five countries.The percentages of respondents who said that they eat out once a week or more as follows:

Germany 10%

France 12%

United Kingdom 28%

Greece 39%

United States 57%

Suppose that the survey was based on 1,000 respondents in each country.

(a)At the 0.05 level of significance,determine whether there is a significant difference in the proportion of people who eat out at least once a week in the various countries.

(b)Find the P-value in(a)and interpret its meaning.

( c)If appropriate,use the Marascuilo procedure and alpha=0.05 to determine which countries are different.Discuss your results.

13.1.Fitting a straight line to a set of data yields the following prediction line:

Ybar i=2+5xi

(a)Interpret the meaning of the Y interpret,b0.

(b)Interpret the meaning of the slope,b1.

( c)Predict the mean value of Y for X=3.

13.2.If the values of X in problem 13.1 range from 2 to 25,should you use this model to predict the mean value of Y when X equals.

(a) 3?

(b) -3?

( c) 0?

(d) 24?

13.4.The marketing manager of a larger supermarket chain would like to use shelf space to predict the sales of pet food.A random sample of 12 equal-sized stores is selected,with the following results.

Shelf Space(X) Weekly Sales(Y)

Store (Feet) ($)

1 5 160

2 5 220

3 5 140

4 10 190

5 10 240

6 10 260

7 15 230

8 15 270

9 15 280

10 20 260

11 20 290

12 20 310

(a)Construct a scatter plot.

For these data,bo=145 and b1=7.4.

(b)Interpret the meaning of the slope,b1,in this problem.

( c)Predict the mean weekly sales of pet food for stores with 8 feet of shelf space for pet food.

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