A development economist is studying income growth in a rural area of a developing country. The last census of the population of this area, several years earlier, showed that mean household annual income was 425 dollars, and the variance of household income was 2500 (dollars-squared). A current random sample of 100 households yields a sample mean income of $433.75. Assume that household annual incomes are approximately normally distributed, and that the population variance is known still to be 2500. Test the null hypothesis that population mean income has not increased against the alternative hypothesis that it has increased, at a 1% level of significance.

What is the form of the rejection region that should be used to conduct this hypothesis test?

Reject

Reject

Reject

Reject Flag this Question Question 2 2 pts

(Continued) What is the critical value in question 1? I.e. what critical value controls the maximum probability of Type I error at 1%?

437.88

433.75

425

436.63

Flag this Question Question 3 2 pts

(Continued) What is the conclusion of the hypothesis test?

Fail to reject the null hypothesis.

Reject the null hypothesis in favor of the alternative hypothesis.

Flag this Question Question 4 2 pts

(Continued) If the population mean is $420, what is the probability the null hypothesis will be rejected (using the rejection region you calculated above)?

Give your answer in the following format: 0.0450 (if it is 0.045) or 0.2345 (if it is for example 0.23452...). I.e. use 4 decimals for your answer.

Flag this Question Question 5 2 pts

(Continued) If the population mean is $430, what is the power of the test (using the rejection region you calculated above)? Use 4 decimals for your answer.

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(Continued) If the population mean is $435, what is the power of the test (using the rejection region you calculated above)? Use 4 decimals for your answer.

Flag this Question Question 7 2 pts

A firm manufactures metal wheels. Diameters of metal wheels produced by this process are approximately normally distributed.

The variance of wheel diameters characteristic of the firm?s old production process is 0.01 (inches-squared). The firm?s engineers have proposed a new process. They claim that the variance of wheel diameters characteristic of the new process is less.

An evaluation team wants to test the null hypothesis that the variance of the new process is no less than the variance of the old process, against the alternative that it is less. In a random sample of size 51, the variance is 0.0042 (inches-squared). The team wants to control the maximum probability of Type I error at 1%.

What is the form of the rejection region?

Reject H_{0} if s^{2} < cv

Reject H_{0} if s^{2} > cv

Reject H_{0} if s^{2} < cv_{1} or if s^{2} > cv_{2}

Reject H_{0} if s^{2} = cv

Flag this Question Question 8 2 pts

(Continue) When calculating the rejection region that controls the maximum probability of Type I error at 1%, the table value you need is the _____ percentile of the _____ random variable.

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