2, Sampling Distribution and Confidence Interval. (10 points) An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be...

Homework problems pasted.


2, Sampling Distribution and Confidence Interval. (10 points) An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 30 individuals resulted in an average income of $15,000. (a) (4 points) Determine the 95% confidence interval estimate of the population mean. (b)(4 points) Determine the 99% confidence interval estimate of the population mean. Suppose you doubt the population standard deviation and from the sample collected, have a sample standard deviation of $800. (c)(2 points) State the assumptions made for each of the confidence intervals you created above. 3, Hypothesis test (25 points, 5 points each) Formulate the null and alternative hypothesis in each case: a. An e-commerce research company claims that 60% or more graduate students have bought merchandise on-line. A consumer group is suspicious of the claim and thinks that the proportion is lower than 60%. b. The administrator at your local hospital states that on weekends the average wait time for emergency room visits is 10 minutes.  Based on discussions you have had with friends who have complained how long they waited to be seen over the weekend, you dispute the administrator's claim.  c. An inventor has developed a new, energy-efficient lawn mower engine. He claims that the engine will run continuously for 300 minutes on a single gallon of regular gasoline. However, you think the engine will not run for 300 minutes on a single gallon. d. The principal of a school thinks that the average IQ of students is 110. 20 students were randomly selected and among the sampled students, the average IQ is 108. You suspect the claim is lower than 110. e. We want to show that children on average have higher cholesterol levels than the national average.  It is known that the mean cholesterol level for all Americans is 190. 4, Hypothesis test and significance test. (20 points, 5 points each) A researcher wants to study the average miles run per day by competitive runners. An old paper says it is 25 miles a day but a researcher thinks otherwise. For this test, a random sample of 36 runners drawn from a normal population whose standard deviation is 10, produced a sample mean of 22.8 miles a day. (a) State the appropriate null and alternative hypotheses. (b) Compute the value of the test statistic and specify the rejection region associated with 5% significance level. Then using the rejection region, test the hypotheses. (c) Compute the p-value. Then using the p-value and 5% significance level, test the hypotheses. (d) Use the confidence interval to test the hypothesis. 5, Hypothesis Test and Significance Test (15 points, 5 points each) A simple random sample of 826 payday loan borrowers was surveyed to better understand their interests around regulation that would require lenders to pull credit reports and evaluate debt payments. 51% of those sampled said they would support regulation. Evaluate whether the poll provides convincing evidence that a majority of payday loan borrowers support regulation. (a) State the appropriate null and alternative hypotheses. (b) Compute the value of the test statistic and specify the rejection region associated with 10% significance level. Then using the rejection region, test the hypotheses. (c) Compute the p-value. Then using the p-value and 10% significance level, test the hypotheses.