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Written Homework Assignment #9 Sections 8.2 8.3 MATH-138 Statistics Directions: On a separate sheet of paper, write out your solutions to the questions below. Then scan your written work, save it as a PDF file, and submit it on Canvas. Late assignments will receive a grade of zero unless prior arrangements are made with me. This assignment is worth 25 points. Do not make these calculations by hand. Instead, use the proper command in your graphing calculator, unless otherwise noted. Write out what you entered in your calculator. If you complete the confidence intervals or probabilities by hand, you will receive no credit for that part of the problem. Do not round your confidence intervals-write down whatever answer the calculator gives you. 1. A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 points, and their standard deviation is 21.4 points. a. Find a 90% confidence interval for the mean score on the test. Be sure to write out what you entered in your calculator. (3 points) b. interpret the interval you found in part a. Round your answers to one decimal place. (2 points) For parts c-c, calculations are not necessary. Deduce the answer from your knowledge of confidence intervals. c. Suppose the standard deviation of the tests had been 42.8 points instead of 21.4 points. What would the larger standard deviation do to the width of the confidence interval? (1 point) d. If the confidence level was increased to 99%, will the interval be wider or narrower? (1 point) e. If the sample size was increased to 75 subjects, will the interval be wider or narrower? (1 point) 2. The principal randomly selected seven students to take an aptitude test. Their scores were: 71.6 81.0 88.9 80.4 78.1 72.0 84.7 a. Find a 95% confidence interval for the mean score on the test. Be sure to write out what you entered in your calculator. (3 points) b. Interpret the interval you found in part a. Round your answers to one decimal place. (2 points)
3. In 2019, the percent of total labor force of the world that were women was about 39%. The United Nations wonders if the percentage of females in the labor force is the same in the United States. Representatives from the United States Department of Labor plan to check a random sample of over 10,000 employment records on file to estimate a percentage of females in the United States labor force. a. They select a random sample of 525 employment records and find that 243 of the people are female. What conditions are required to construct a confidence interval? (1 point) b. Create a 90% confidence interval. Be sure to write out what you entered in your calculator. (3 points) c. Use your confidence interval to find the margin of error. Round your answer to 4 decimal places. (1 point) d. Interpret the confidence interval in this context. Round your answers to one decimal place. (2 points) e. Should the representatives from the Department of Labor conclude that the percentage of females in their labor force is higher than the world's rate of 39%? Explain. (2 points) 4. A survey of shoppers is planned to see what percentage use credit cards. Prior surveys suggest that 72% of shoppers use credit cards. How many randomly selected shoppers must we survey in order to estimate the proportion of shoppers who use credit cards to within 4% with 98% confidence? Be sure to show all your work and round appropriately. (3 points)