Statistic Problems

Must show work on how problem was solved on all questions!

The following problem statement is to be used for problems 16 through 19.

How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: X-bar= 52, s= 22.

16. State the null and alternative hypotheses to determine if the number of tissues used during a cold is less than 60.

17. Using the sample information provided, calculate the value of the test statistic.

18. Suppose the alternative we wanted to test was H1:  < 60. State the

correct rejection region for  = 0.05.

a. Reject H0if t> 1.6604.

b. Reject H0if t< -1.6604.

c. Reject H0if t> 1.9842 or t< -1.9842.

d. Reject H0if t< -1.9842.

19. Suppose the test statistic does fall in the rejection region at

α = 0.05.

The following problem statement is to be used for problems 21 and 22

The owner of a local night club has recently surveyed a random sample of n= 250 customers of the club. She would now like to determine whether the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made.

21. With regard to the above problem statement, the appropriate hypotheses to test are:

a. H0: μ > 30 versus H1: μ < 30

b. H0: μ < 30 versus H1: μ > 30

c. H0: X> 30 versus H1: X< 30

d. H0: X< 30 versus H1: X> 30

22. With regard to the above problem statement, suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. What is the pvalue associated with the test statistic? (assume that the Central Limit Theorem applies)

a. 0.3577

b. 0.1423

c. 0.0778

d. 0.02

Problem 33

A political pollster randomly selects a sample of 100 voters each day for 8 successive days and asks how many will vote for the incumbent. The pollster wishes to construct a p chart to see if the percentage favoring the incumbent candidate is too erratic.

Sample Number Favoring

(Day) Incumbent Candidate

1 57

2 57

3 53

4 51

5 55

6 60

7 56

8 59

a. Referring to the problem statement, what is the numerical value of the center line for the p chart?

b. Referring to the problem statement, what is the numerical value of the lower control limit for the p chart?

c. Referring to the problem statement, what is the numerical value of the upper control limit for the p chart?

Problem 34

A factory supervisor is concerned that the time it takes workers to complete an important production task (measured in seconds) is too erratic and adversely affects expected profits. The supervisor proceeds by randomly sampling 5 individuals per hour for a period of 10 hours. The sample mean and range for each hour are listed below.

Hour X R

1 18.4 25

2 16.9 27

3 23.0 30

4 21.2 23

5 21.0 24

6 24.0 25

7 19.3 12

8 15.8 14

9 20.0 13

10 23.0 11

a. Referring to the problem statement, suppose the supervisor constructs an R chart to see if the variability in collection times is in-control. What is the center line of this R chart?

b. Referring to the problem statement, suppose the supervisor constructs an R chart to see if the variability in collection times is in-control. What are the lower and upper control limits for this R chart?

c. Referring to the problem statement, suppose the sample mean and range data were based on 6 observations per hour instead of 5. How would this change affect the lower and upper control limits of an R chart?

a. LCL would increase; UCL would decrease.

b. LCL would remain the same; UCL would decrease.

c. Both LCL and UCL would remain the same.

d. LCL would decrease; UCL would increase.

d. Referring to the problem statement, suppose the supervisor constructs an X-barchart to see if the process is in-control. What is the center line of the chart?

e. Referring to the problem statement, suppose the supervisor constructs an X-barchart to see if the process is in-control. What are the lower and upper control limits of this chart?

The following problem statement is to be used for problems 43 through 48.

An appliance manufacturer claims to have developed a compact microwave oven that consumes an average of no more than 250 W. From previous studies, it was determined that power consumption for microwave ovens is normally distributed with a standard deviation of 15 W. A consumer group has decided to try to discover if the claim appears true. They take a sample of 20 microwave ovens and find that they consume an average of 257.3 W.

43. Referring to the problem statement, the appropriate hypotheses to determine if the manufacturer's claim appears reasonable are:

a. H0: μ = 250 versus H1: μ  250

b. H0: μ  250 versus H1: μ < 250

c. H0: μ  250 versus H1: μ > 250

d. H0: μ  257.3 versus H1: μ < 257.3

44. Referring to the problem statement, for a test with a level of significance of 0.05, the critical value would be ________.

45. Referring to the problem statement, the value of the test statistic is ________.

46. Referring to the problem statement, the p value of the test is ________.

52. Assuming a linear relationship between Xand Y, if SSX is positive and SSXY is negative

a. there is no correlation.

b. the slope (b1)is negative.

c. variable Xis larger than variable Y.

d. the variance of Xis negative.

63. The value of the coefficient of determination may be either positive or negative.

a. True

b. False

The following problem statement is to be used for problems 64 through 70.

The managing partner of an advertising agency believes that his company's sales are related to the industry sales. He uses Microsoft Excel's Data Analysis tool to analyze the last four years of quarterly data (i.e., n= 16) with the following results:

Regression Statistics

Multiple R 0.802

R Square 0.643

Adjusted R Square 0.618

Standard Error SYX 0.9224

Observations 16

ANOVA

df SS MS F Sig.F(p-value)

Regression 1 21.497 21.497 25.27 0.000

Error 14 11.912 0.851

Total 15 33.409

Predictor Coef StdError t Stat P-value

Intercept 3.962 1.440 2.75 0.016

Industry(slope) 0.040451 0.008048 5.03 0.000

64. Referring to the problem statement, the value of the quantity that the least squares regression line minimizes is ________.

65. Referring to the problem statement, the estimates of the Y-intercept and slope are ________ and ________, respectively.

66. Referring to the problem statement, the prediction for a quarter in which X= 120 is Y = ________.

67. Referring to the problem statement, the value for the standard error of the estimate is ________.

68. Referring to the problem statement, the value of the coefficient of determination is ________.

69. Referring to the problem statement, the value of the adjusted coefficient of determination is ________.

70. Referring to the problem statement, value of the standard error of the slope is ________.

80.For all of the questions that follow, you may leave the answer in terms of pi, if you wish or you may assume that pi = 3.14 – either approach is fine. The equation for the circumference of a circle is (pi)*(Diameter).

a. Suppose we have an orange that is three inches in diameter. We stretch a string around its circumference. What is the length of the string? (assume that the orange is a perfect sphere.)

b. Now, suppose we raise the string two inches above the orange, all the way around (i.e. we have the string two inches above the surface of the orange all the way around). What is the new length of the string, and what is the difference in the answers between part a and part b?

c. Now suppose we stretch another string all the way around the circumference of the earth. What is the length of the string? (assume the earth is a perfect sphere that is 24,000 miles in diameter)

d. Now, suppose the string is raised two inches above the earth, all the way around. What is the new length and what is the difference between part c and part d? Compare the differences between the increase in string length for the orange vs the increase in string length for the earth. What can you conclude?