One sample t test and Confidence Interval for the population mean.
A Wendy's franchise has been averaging about $5000 worth of business on a typical Saturday with a standard deviation of σ = $500. The manager is concerned that sales are slipping, after taking into account the average value of sales for four consecutive Saturdays being $4800.
a. Formulate an appropriate hypothesis test to examine at the 10 percent level of significance whether the manager's worries are justified.
b. What should the level of significance be to arrive at an end?
c. Based on the sample findings, estimate the true mean of Saturday sales with 90 percent probability.
d. If we wanted to shorten the interval of the estimation of the true mean of Saturday sales to a width of $600 in total, what should the size of our sample be to achieve it?
e. If the true mean for Saturday sales is now $4500, what is the likelihood of accepting the (false) null hypothesis in (a) above (the probability of not sharing the manager's concern because of lack of evidence)?