Neiman Marcus, a high end retailer, is interested in an opening a shop in Little Rock. Before they open the shop they are interested in finding out the average income in Little Rock. You are assigned this project and you sample 100 households in Little Rock and you discover that their average income is $50,000 with a sample standard deviation of $2,000. Neiman Marcus wants you to construct an 80%,95%, and a 99% Confidence Interval for income in Little Rock.

Fuel efficiency of Prius:  Fueleconomy.gov, the official US government source for fuel economy information, allows users to share gas mileage information on their vehicles. The histogram below shows the distribution of gas mileage in miles per gallon (MPG) from 14 users who drive a 2012 Toyota Prius. The sample mean is 53.3 MPG and the standard deviation is 5.2 MPG. Note that these data are user estimates and since the source data cannot be verified, the accuracy of these estimates are not guaranteed. (a) The EPA claims that a 2012 Prius gets 50 MPG (city and highway mileage combined). Do these data provide strong evidence against this estimate for drivers who participate on fueleconomy.gov? The test statistic is: __________________(please round to two decimal places)The p-value:___________________________ for this hypothesis test is:  (please round to four decimal places)(c) Please comment on the primary thing that is wrong about the following statement: There is sufficient evidence…

In a survey, 22 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $50 and standard deviation of $8. Construct a confidence interval at a 90% confidence level.Give your answers to one decimal place.

In a survey, 14 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $36 and standard deviation of $16. Construct a confidence interval at a 99% confidence level. Give your answers to one decimal place.

In a survey, 15 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $47 and standard deviation of $10. Construct a confidence interval at a 95% confidence level.Give your answers to one decimal place.

In a survey, 21 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $32 and standard deviation of $8. Construct a confidence interval at a 99% confidence level. Give your answers to one decimal place.

In a survey, 19 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $49 and standard deviation of $2. Construct a confidence interval at a 99% confidence level. Give your answers to one decimal place. Interpret your confidence interval in the context of this problem.