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# Confidence interval and P value calculation

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1. The business college computing center wants to determine the proportion of business students who have personal computers at home. If the proportion exceeds 30%, then the lab will scale back a proposed enlargement of its facilities. Suppose 250 business students were randomly sampled and 75 have pcs at home. Find the rejection region using a = 0.05

a. Reject Ho if z < -1.645
b. Reject Ho if Z = 1.645
c. Reject Ho if Z > 1.645
d. Reject Ho if Z >1.96 or z < - 1.96

2. In the test of hypothesis Ho mean= 50 and Ha mean not equal to 50, a sample of n = 100 observations possessed the mean x = 50.3 and standard deviation s = 2.1. Find the p-value for this test.

a. 0.0764
b. 0.8472
c. 0.1556
d. 0.1528

3. a local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful if the average time spent on the deliveries does not exceed 27 minutes. The owner has randomly selected 23 customers and has delivered pizzas to their homes in order to test if the mean delivery time actually exceeds 27 minutes. Suppose the p-value for the test was found to be 0.2071. state the conclusion

a. At a = 0.03, we fail to reject Ho.

b. At a = 0.02, we reject Ho.

c. At a = 0.025, we fail to reject Ho.

d. At a = 0.05, we fail to reject Ho.

4. In a test of hypothesis Ho: mean = 20 and Ha mean not equal to 20, a sample of 50 observations possessed the mean x = 19.4 and standard deviation s =3.1. Find the p-value for the test.

a. 0.9131
b. 0.0869
c. 0.0853
d. 0.9147