Exam 9: Large-Sample Tests of Hypotheses

An insurance company wants to test the hypothesis that the mean amount of life insurance held by professional men equals that held by professional women. Accordingly, two independent simple random samples are taken from appropriate professional listings of men and women. The sample of 200 men reveals a mean amount of $140,000 with a standard deviation $26,000. The sample of 400 women shows a mean amount of $128,000 with a standard deviation of $3,000. Test the hypothesis using a 0.05 significance level. Test statistic = ______________ p-value = ______________ Critical Value(s) = ______________ Conclusion: ______________ Interpretation: __________________________________________ Construct 95% confidence interval for the difference in mean amount of life insurance held by professional men and women. ______________ Explain how to use the 95% confidence interval to test the appropriate hypotheses at = 0.05. __________________________________________

Let denote the true average delivery time of a letter from a specific carrier. For a large-sample z test of H₀: = 3 versus H_a: 3, find the p-value associated with each of the given values of the test statistic, and state whether each p-value will lead to a rejection of the null hypothesis when performing a level 0.05 test. = 2.16 p = ______________ Conclusion: ______________ = 0.38 p = ______________ Conclusion: ______________ = -2.81 p = ______________ Conclusion: ______________ = 1.07 p = ______________ Conclusion: ______________ = -0.68 p = ______________ Conclusion: ______________

In testing vs. the test statistic value is found to be z = 1.28. The p-value of the test is approximately .1003.

When the necessary conditions are met, an upper tailed test is being conducted for the difference between two population proportions. If the value of the test statistic is 2.90, then the p-value is 0.0038.

The width of a confidence interval estimate for a proportion will be:

The lower limit of the 90% confidence interval for the population proportion p, given that n = 400 and = 0.10 is 0.1247.

Which of the following statements is true?

Which of the following statements about the null hypothesis is false?

A quality control officer tests bottles of shampoo to see if the filling machines are putting the proper amount in each bottle. They do not want to shut down production unless there is strong evidence indicating that the machines are not functioning properly. After testing a sample of bottles, the quality control officer decides to leave the filling machines operating. Actually, however, the filling machines are not operating properly. Which type of error, if any, did the quality control officer commit?

From a sample of 400 items, 14 are found to be defective. The point estimate of the population proportion defective will be: