Question

Brand managers become concerned if they discover that customers are aging and gradually moving out of the high-spending age groups. For example, the average Cadillac buyer is older than 60, past the prime middle years that typically are associated with more spending. Part of the importance to Cadillac of the success of the Escalade model has been its ability to draw in younger customers. If a sample of 50 Escalade purchasers has average age 45 (with standard deviation 25), is this com pelling evidence that Escalade buyers are younger on average than the typical Cadillac buyer? (Assume that the data meet the sample size condition.)

(a) State the null and alternative hypotheses. Describe the parameters.

(b) Identify the Type I (false positive) and Type II (false negative) errors.

Answer 1

Explanation:

a) The null hypothesis is the hypothesis that is assumed to be true. In this situation, the null hypothesis is "the average Cadillac buyer is older than 60". It is written as

H0: µ ≥ 60

The alternative hypothesis is what the researcher expects or predicts. It is the statement that is believed to be true if the null hypothesis is rejected. In this situation, the alternative hypothesis is "Escalade buyers are younger on average than the typical Cadillac buyer". It is written as

H1: µ < 60

The parameters are

Population mean = 60

Sample mean = 45

number of samples = 50

Standard deviation = 25

b) The type 1 error occurs if a true null hypothesis is rejected. In this situation, type 1 error is accepting that the the average Escalade buyers are younger on average than the typical Cadillac buyer when they are actually older.

Type II error occurs when a false null hypothesis is accepted. In this situation, type II error is accepting that the average Cadillac buyer is older than 60 when they are actually younger.