Reference no: EM132413620

Suppose that the manager of the Mileage Plus frequent flier program is promoted and consequently another individual is hired to replace him/her/xhe. Also suppose that United publishes in internal documentation that the average number of Premier Qualifying Miles (PQM) earned by individuals who travel for work at least once a month is 55,000 with a standard deviation of 5,000 miles. Further suppose that the new manager desires to test the claims that United has made to see if the statistics have changed.

a. First, are these statistics given by United describing the parent population or a sample?

b. Define appropriate null and alternative hypotheses.

c. Suppose that the new manager takes a sample of 50 such United customers. What is the probability that a sample of size 50 provides a sample mean within ± 1,000 miles of the 55,000 mile figure provided by United?

d. What is the probability that a sample of 50 such United customers provides a sample mean within ± 500 miles?

e. Suppose that the new manager's sample has a sample has a sample average of 57,500 miles. Compute the 95% confidence interval for the population mean.

f. Based on the confidence interval you computed in part (e), does this sample provide evidence for or against United's claim that the average number of premier Qualifying Miles (PQM) earned is 55,000?

g. If the new manager wants to determine a specific p-value for the likelihood that the null hypothesis is true based on the sample collected in part (c), should he/she/xhe use Z- or t- scores for the test statistic?

h. Determine and interpret the p-value.