Question 1: You work for a consumer advocate agency and want to find the mean repair cost of a washing machine. As part of your study, you randomly select 45 repair costs and find the mean to be $104.50. Assume the population standard deviation is $17.50.
a. Construct a 95% confidence interval for the population mean repair cost of a washing machine.
b. Based on your confidence interval, can you say the mean repair cost of a washing machine is greater than $100?
Question 2: Your instructor has decided to run for Mayor. He has no idea how many people will vote for him, so he wants to conduct a survey. Determine the minimum sample size necessary so he can be 95% confident that the proportion of voters who will vote for him is accurate within 4% of the population proportion?
Question 3: A college administrator wants to estimate the mean cost of textbooks for students per semester. Determine the minimum sample size required so the administrator can be 95% confident that the average cost of textbooks per student per semester is within $20 of the population mean. Assume standard deviation: $100.
Question 4: Data from a representative sample were used to estimate that 32% of all computer users in 2011 had tried to get on a Wi-Fi network that was not their own in order to save money. You decide to conduct a survey to estimate this proportion for the current year. Determine the minimum sample size needed so you can be 99% confident the proportion is within 5% of the population proportion.
Question 5: State which distribution should be used with the given information: normal (z), Student’s t, or neither.
a. A simple random sample of 45 Macintosh apples were weighed and found to have a mean of 10 ounces with a standard deviation of 2 ounces. Determine a 90% confidence interval estimate for the mean weight of Macintosh apples. Circle the correct distribution used to complete this exercise:
normal (z) Student’s t neither
b. A simple random sample of 15 students were asked how much money was in their pockets. The average was $18.75 and the standard deviation was $4.91. Find a 99% confidence interval. Circle the correct distribution used to complete this exercise:
normal (z) Student’s t neither
c. A simple random sample of 10 large American cities found a sample mean number of HIV-related deaths per week of 42 and a sample standard deviation of 12. Assume that the numbers of HIV-related deaths are normally distributed. Find a 95% confidence interval. Circle the correct distribution used to complete this exercise:
normal (z) Student’s t neither
