NAME: _______________________

Date:________________________

REVIEW PROBLEMS SET-3

QUESTIONS 1-8 The Interstate Conference of Employment Security Agencies is conducting a study to determine the number of hours per week worked in the United States. A mean of 36 hours per week was obtained from a random sample of 20 workers and the standard deviation of the sample was 8 hours. Assume hours worked per week are normally distributed in the population. Q1. The point estimate of the mean number of hours worked by the population US workers is: _______ Q2. The margin of error for a 99% confidence interval for the mean number of hours worked per week for the population of US workers is _________

Q3. The 90% confidence interval for the mean number of hours worked per week for the population of US workers is _________________ Suppose the agency believes the average workweek in the United States has decreased from the traditional 40hrs per week largely because of a rise in part-time workers and they will use this sample on to conduct a hypothesis test.

Q4. Which of the following pairs of hypotheses will they need to test ? Why a) Ho : µ >=36 ; Ha : µ < 36 b) Ho : µ = 36 ; Ha : µ ≠ 36 c) Ho : µ >=40 ; Ha : µ < 40 d) Ho : µ = 40 ; Ha : µ ≠ 40 e) None of the above

Q5. What is the p-value for their test ?

Q6 What is the value of the test statistic ?

Q7. Using a significance level alpha=5%, the correct conclusion is : a) Reject Ho, there is no significant evidence that the average number of hours per week has decreased. b) Reject Ho, there is evidence that the average number of hours per week has decreased. c) Do not Reject Ho, there is evidence that the average number of hours per week has decreased. d) Do not Reject Ho, there is no evidence that the average number of hours per week has decreased.

Q8. Using a significance level alpha=1%, the correct conclusion is : a) Reject Ho, there is no significant evidence that the average number of hours per week has decreased. b) Reject Ho, there is evidence that the average number of hours per week has decreased. c) Do not Reject Ho, there is evidence that the average number of hours per week has decreased. d) Do not Reject Ho, there is no evidence that the average number of hours per week has decreased.

QUESTIONS 9 Compute a 95% confidence interval for the population proportion for a sample size = 200 and a sample proportion = 25%

QUESTION 10 What is the margin of error of a 99% confidence interval for the population mean based on the following info: X= 15, σ=4, n=10.? QUESTION 11. What is the margin of error of a 99% confidence interval for the population mean based on the following info: X= 15, s=4, n=10.?

NAME: _______________________

Date:________________________ QUESTIONS 12-14 A company wishes to determine if their training program is helping workers perform better on their industrial plant. Four workers are selected at random to undergo the training. The four workers take a performance test prior to the training and another one after the training. The scores are given below.

Worker’s score 1 2 3 4

First score 450 520 720 600

Second score 440 600 720 630

Assume that the change in score (second score – first score) for the population of all workers is normally distributed with mean μ. Q12. The margin of error of a 99% confidence interval for μ is (Use 3 decimals) Q13. What is the p-value for testing the hypothesis that the training has been effective in improving the performance of workers ? Q14. Is there significant evidence at the 1% level that the training has been effective in improving the performance of workers ? QUESTIONS 15 A store manager wants to use a 95% confidence interval to estimate the average total monthly purchases per customer at the store within $20 of the actual average. Historical data shows that the standard deviation of total monthly sales for all customers is about $40. How large a sample do they need ? QUESTION 16 A study will be conducted to construct a 90% confidence interval for a population proportion. An error of 0.03 is desired. There is no knowledge as to what the population proportion will be. What sample size is required ? QUESTIONS 17-20 A plant manufactures digital components that are supposed to be 15mm in length. The quality control department periodically checks the process to determine if length of components produced is in accordance with specifications. If the components do not comply with the required length, the process needs adjustment. Suppose five components are randomly selected and their average length is 13mm with a standard deviation of 4mm. Q17. What would be the conclusion using a significant level alpha= 5%.

a) Reject Ho, the process needs adjustment. b) Reject Ho, the process DOES NOT need adjustment. c) Do not Reject Ho, the process needs adjustment. d) Do not Reject Ho, the process DOES NOT need adjustment.

Q18. What is the p-value of the hypothesis test ? Q19. What is the value of the test statistic ? Q20. Will the conclusion be the same using a significance level alpha =1% ?

INDEX

SAMPLE SIZE For MEANS

SAMPLE SIZE For PROPORTIONS

CI -MEAN-σ KNOWN - using Z

CI -MEAN-σ UNKNOWN - using t

CI-ONE PROPORTION

CI -TWO MEANS-σ KNOWN

CI -TWO MEANS-σ UNKNOWN

CI-TWO PROPORTIONS

Z TEST-ONE MEAN-σ KNOWN

T TEST-ONE MEAN-σ UNKNOWN

Z TEST-PROPORTION

Z TEST-TWO MEANS-σ KNOWN

T TEST-TWO MEANS-σ UNKNOWN

Z TEST - TWO PROPORTIONS