T-Mobile 9:01 PM 1% bluequill.franklin.edu Math 215 Statistical Concepts Name: Franklin University HOW DO YOU MAKE INFORMED DECISIONS? Problem 1: (5 points) Many people claim that they can put a meal on the table in a short period of time. However, an article at USA Today in 2006 reported that people usually spend an average of 40 minutes for preparing dinner. A culinary expert wanted to conduct a study to test the validity of this statement. She selected a random sample of 30 people (male and female) and timed them as they made dinner. Their length of time (in minutes) to prepare and cook dinner is recorded, with the following results: 44.3 51.8 49.8 40.1 55.5 33.2 43.4 41.4 45.5 40.7 41.6 49.0 30.8 45.4 55.3 52.2 55.6 38.4 43.2 39.1 58.6 49.8 43.2 47.9 46.6 38.5 43.6 51.0 47.4 36.7 a. Is there a significant evidence that the population mean time to prepare and cook dinner is more than 40 minutes? Use a hypothesis test with a 0.05 to make an informed decision. Show all steps of the hypothesis test being used with your calculator commands. = b. Find a 95% and confidence interval for the population mean time to cook and prepare dinner. Show your work or calculator commands. What is the margin of error? What can be done to make this margin of error smaller? Problem 2: (5 points) A market research survey asked the question "Do you enjoy shopping for clothing for yourself?" to 542 male adults and 238 of them said they did. When 543 female adults were asked the same question, 276 of them indicated that they enjoyed shopping for clothing for themselves. (Source: USA Today) a. Is there a significant difference between the proportion of males and females who enjoy shopping for clothing for themselves at the 0.05 level of significance? Perform a hypothesis test with all its steps to make an informed decision. Show your work or calculator commands. b. Find a 95% and confidence interval for the difference between the proportions of males and females who enjoy shopping for clothing for themselves. Show your work or calculator commands. Does this interval support your decision in part a?