Week 13 Discussion Questions STAT 400 Spring 2022 D Unger Table of Contents Exercise 1 Hypothesis Test for p 1 Exercise 2 Hypothesis Test for p 1 Exercise 3 Hypothesis Test for 1 2 2 Exercise 4 Hypothesis Test for 1 2 2 Exercise 5 Hypothesis Test for p1 p2 3 Exercise 6 Hypothesis Test for p1 p2 3 Exercise 7 Hypothesis Test for 4 Exercise 8 Hypothesis Test for 4 Exercise 1 Hypothesis Test for p In a random sample of 160 students from Faber College 56 believe that resume inflation i e misrepresenting yourself on your resume is unethical a Find the p value of the test H0 p 0 40 versus H1 p 0 40 b Is there significant evidence to suggest that fewer than 2 out of every 5 students think resume inflation is unethical at the 0 10 level of significance Exercise 2 Hypothesis Test for p An economist states that 10 of Champaign Urbana s labor force is unemployed A random sample of 400 people in the labor force is obtained of whom 28 are unemployed a Test whether Champaign Urbana s unemployment rate is as the economist claims or is different than the claim at a 1 level of significance using the critical region method for evidence b Find the p value of the test in part a c Using the p value from part b state your decision at 0 05 Exercise 3 Hypothesis Test for 1 2 A random sample of 9 adult white rhinos had the sample mean weight of 5 100 pounds and the sample standard deviation of 450 pounds A random sample of 16 adult hippos had the sample mean weight of 3 300 pounds and the sample standard deviation of 400 pounds Assume that the two populations are approximately normally distributed a Construct a 95 confidence interval for the difference between their overall average weights of adult white rhinos and adult hippos i Assume the population standard deviations are equal ii Assume the population standard deviations are not equal and use the conservative approach iii Assume the population standard deviations are not equal and use Welch s T b It s believed that on average an adult white rhino weighs 1 500 pounds more than an adult hippo Test this claim against an alternative hypothesis that the average weight difference is greater than 1 500 pounds at an 0 05 level of significance Assume that the population standard deviations are equal Exercise 4 Hypothesis Test for 1 2 A researcher wishes to determine whether the starting salaries of high school math teachers in private schools are higher than those of high school math teachers in public schools She selects a sample of new math teachers from each type of school and calculates the sample means and sample standard deviations of their salaries For private schools the sample of size 10 yielded a sample mean of 36 800 and sample standard deviation of 600 For public schools the sample of size 7 yielded a sample mean of 36 300 and sample standard deviation of 546 Assume that the populations are normally distributed and the population variances are equal a Construct a 95 confidence interval for the difference in average starting salaries of high school math teachers in private and public schools b By the null hypothesis there would be no difference between the salaries of the two groups Test the researcher s theory that the starting salaries of high school math teachers in private schools are higher than those of high school math teachers in public schools Use a 1 level of significance and the critical region method c Find the p value of the test in part b Exercise 5 Hypothesis Test for p1 p2 Students wishing to become actuaries must take a series of professional examinations The first is called Exam P Probability and the second is called Exam FM Financial Mathematics In a random sample of 200 students who took Exam P last year 74 successfully passed the exam Suppose also that in a random sample of 150 students who took Exam FM 45 successfully passed the exam a Construct a 95 confidence interval for the difference between the overall proportions of students who passed Exam P and Exam FM last year b At a 10 level of significance test whether Exam P had a higher success rate than Exam FM last year Find the p value of this test Exercise 6 Hypothesis Test for p1 p2 In a comparative study of two new pain relief drugs labeled A and B 120 patients were treated with drug A and 150 patients with drug B and the following results were obtained Drug A Drug B Pain relief within 10 minutes No pain relief within 10 minutes pain relief after more than 10 minutes 78 42 111 39 Total 120 150 a Construct a 95 confidence interval for the difference in pain relief rates of the two drugs b We wish to test whether drug B has a better pain relief rate than drug A Find the p value of the appropriate test and make a decision at the 0 05 level of significance Exercise 7 Hypothesis Test for An examination of the records for a random sample of 16 motor vehicles in a large fleet resulted in the sample mean operating cost of 26 33 cents per mile and the sample standard deviation of 2 80 cents per mile Assume that operating costs are approximately normally distributed a Test whether the overall standard deviation of the operating costs is more than 2 30 cents per mile or not at a 5 significance level b Using the Chi Square Distribution table what is the p value of the test in part a You may give a range c Use a computer with R or an appropriate calculator to find the p value of the test in part a Exercise 8 Hypothesis Test for Several employees of Al s Building Construction complain that the variance of the employees monthly salary amounts is too large In a random sample of 10 employees the sample standard deviation of the monthly salary amounts was 210 a Use 0 05 to test H0 150 vs H1 150 Report the value of the test statistic the critical value s and state your decision b Using the Chi Square Distribution table what is the p value of the test in part a You may give a range c Use a computer with R or an appropriate calculator to find the p value of the test in part a
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