Review for TEST I



Review for TEST II

Make sure to identify all elements of Test of Hypothesis and Confidence Interval, such as :

Point estimator, Sampling Error, Test statistic, Critical value, P-value, Rejection Region, Level of significance, Error type I and II, Null and Alternate hypotheses, Assumptions. Good luck!

1. A salesman for a shoe company claimed that runners would record quicker times, on the average, with the company's brand of sneaker. A track coach decided to test the claim. The coach selected eight runners. Each runner ran two 100-yard dashes on different days. In one 100-yard dash, the runners wore the sneakers supplied by the school; in the other, they wore the sneakers supplied by the salesman. Each runner was randomly assigned the sneakers to wear for the first run. Their times, measured in seconds, were as follows:

|Sneakers |1 |2 |

|Sample size |35 |35 |

|Mean Pain Reduction |0.49 |0.44 |

|Standard Deviation |0.96 |1.4 |

5. A study at the University of Michigan wants to determine student options regarding non-revenue-generating athletics. Specifically, one question in a survey asks students "Do you think the women's basketball program should be discontinued?" The data collected revealed that 100 of the 1,000 females surveyed responded "Yes" and that 400 of the 1,000 males surveyed responded "Yes". Suppose a 99% confidence interval resulted in the following confidence interval for the true difference in population proportions: (-.5, -.1). Interpret the interval.

What is value of the point estimator? ______ What is the value of margin of error? _______

6. How does wives' employment status affect their husbands' well being? To answer this question, a survey of the job satisfaction of 25 male accountants who were employed full-time and married was conducted. In this sample, 15 wives were employed and 10 were unemployed. The goal of the study is to compare the mean job satisfaction levels of the two groups of husbands: (1) those with working wives and (2) those with unemployed wives. The observed significance level (p-value) of the test is .03. Is this sufficient evidence to conclude that the mean satisfaction level of husbands with working wives is less than the mean satisfaction level of husbands with unemployed wives? Test using [pic]=.05.

7. In a study of the accuracy of telephone surveys, 720 people out of 1720 refused to respond during a standard five day survey. In the same study, 429 people out of 1640 refused to respond during a rigorous eight week survey. Use a 0.01 significance level to test the claim that the refusal rate is lower with the rigorous survey.

8.  In a test of Ho:[pic] versus Ha:[pic], the p-value=0.042. Use α = .03.

There is (sufficient / insufficient) evidence to conclude that P1 is (greater / less) than P2.

9. A weight-lifting coach claims that weight-lifters can increase their strength by taking a certain supplement. To test the theory, the coach randomly selects 9 athletes and gives them a strength test using a bench press. The results are listed below. Thirty days later, after regular training using the supplement, they are tested again. The new results are listed below. Test the claim that the supplement is effective in increasing the athletes' strength.

|Athlete |

32. We are interested in comparing the average supermarket prices of two leading colas in the Tampa area. Our sample was taken by randomly going to each of eight supermarkets and recording the price of a six-pack of cola of each brand. The data are shown in the following table:

Price

[pic]

If the data above was collected thorough a paired difference experiment, what assumptions are needed to make valid inferences about the mean difference of cola prices?

33. The newspaper recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did the men. One question asked of both men and women was "Do you think sexual harassment is a major problem in the American workplace?" 24% of the men and 62% of the women responded "Yes." The newspaper created a 99.2% confidence interval for the true difference in proportions and reported it to be -.28 to -.48. What can be said about the proportions with 99.2% reliability?

34. A sociologist wants to determine whether the proportion of women who favor the death penalty differs from the proportion of men who favor the death penalty. He will randomly select 100 men and 125 women. Each person will be asked whether he/she favors the death penalty.

a. Independent samples z-test c. Test for two proportions

b. Independent samples t-test e. Matched pairs t-test

35. A gambler has developed two strategies for betting in the game of blackjack. To test these strategies, he decides to go gambling on a casino boat. He plays five sessions of blackjack with each strategy, with each session consisting of 20 hands. He then records the profits of each session. Please note that a negative profit indicates a loss. The computer output used in this analysis is shown below. The goal of the gambler is to determine, if possible, which of the two betting strategies will result in a higher mean profit.

[pic]

Ho: μ1 - μ2 > 0 versus Ha: μ1 - μ2 < 0

[pic]

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