Solve and paper work only plz

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 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. (2 points) c. Suppose the test's standard deviation was 42.8 points instead of 21.4. Would the larger standard deviation increase or decrease the width of the confidence interval? (1 point) d. If the confidence level were reduced to 90%, will the interval be wider or narrower? I point) 2. 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. They select a random sample of 525 employment records and find that 229 of the people are female. Create a 90% confidence interval. Write all calculator commands - no hand calculations allowed. (3 points) b. Interpret the confidence interval in this context. (2 points) c. Use your interval to find the margin of error associated with this confidence interval. (1 point) d. 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) 3. A survey of shoppers is planned to see what percentage use credit cards. Prior surveys suggest that 54% of shoppers use credit cards. How many randomly selected shoppers must we survey to estimate the proportion of shoppers who use credit cards to within 3% with 98% confidence? Be sure to show all your work and round appropriately. (4 points)