Mutual Savings Bank of Appleton has done a market research survey in which people were asked to rate their image of the bank on a scale of 1 to 10, with 10 being the most favorable. The mean response for the sample of 400 people was 7.25, with a standard deviation of 2.51. On this same question a state association of mutual savings banks has found a mean of 7.01.
a. Clara Wharton, marketing director for the bank, would like to test to see whether the rating for her bank is significantly greater than the norm of 7.01. Perform the appropriate hypothesis test for a 95 percent confidence level.
b. Draw a diagram to illustrate your result.
c. How would your result be affected if the sample size had been 100 rather than 400, with everything else being the same?