1. A sample of 9 days over the past six months showed that a clinic treated the following numbers of patients: 24, 26, 21, 17, 16, 23, 27, 18, and 25. If the number of patients seen per day is normally distributed, would an analysis of these sample data provide evidence that the variance in the number of patients seen per day is less than 10? Use α = .025 level of significance. What is your conclusion using p-value and critical value approaches. Is the conclusion different in both the cases?
2. At Western University the historical mean of scholarship examination score for freshman applications is 900. Population standard deviation is assumed to be known as 180. Each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed.
a) State the hypotheses.
b) What is the 95% confidence interval estimate of the population mean examination score if a sample of 100 applications provided a sample mean 935?
c) Use the confidence interval approach to conduct a hypothesis test. What is your conclusion?
d) Assuming α = .05, conduct p-value based and critical-value based hypothesis tests. How do the results compare in all the three cases?
3. The grade point averages of 61 students who completed a college course in financial accounting have a standard deviation of .790. The grade point averages of 17 students who dropped out of the same course have a standard deviation of .940. Do the data indicate a difference between the variances of grade point averages for students who completed a financial accounting course and students who dropped out? Use α = .05 level of significance. Use both p-value and critical value approaches. Compare the test results.
4. The following data were collected on the number of emergency ambulance calls for an urban county and a rural county in Florida. Is County type independent of the day of the week in receiving the emergency ambulance calls? Use α = 0.005. What is your conclusion?
Day of the Week
Sun Mon Tue Wed Thu Fri Sat
County
Urban 62 47 48 51 61 74 41
Rural 6 10 18 17 11 13 12
5. Medical tests were conducted to learn about drug-resistant tuberculosis. Of 284 cases tested in New Jersey, 18 were found to be drug- resistant. Of 536 cases tested in Texas, 10 were found to be drugresistant. Do these data indicate that New Jersey has a statistically significant higher outbreak of drugresistant tuberculosis cases? Use a .03 level of significance. What is the p- value, and what is your conclusion? Is the conclusion any different under critical-value approach?
6. Consider the following data for two independent random samples taken from two normal populations.
Sample 1 14 26 20 16 14 18
Sample 2 18 16 8 12 16 14
a) Compute the two sample means and the two sample standard deviations.
b) What is the point estimate of the difference between the two population means?
c) Assuming α = .10, conduct p-value based and critical-value based hypothesis tests for the equality of means of the two populations.
d) What is the 90% confidence interval estimate of the difference between the two population means? How do the results compare in all the three approaches to hypothesis testing?