P-value and test statistic for Haug Motor Company

Marketing executives at Haug Motor Company, producers of the world's most imposing SUVs, are planning their sales campaign for a new model, the 6000 lb. Enviroraptor MPG-8?. They are staking their hopes on the belief that the average American is more interested in personal aggrandizement than in the environment or public safety. They feel that the average score on the Pearson Self-Absorption Test is at least 92. It is assumed that the population standard deviation is 14. They will conduct a test and discard their hypothesis only if the sample data contradicts it at the .02 level. A random sample of 50 potential customers yields a mean score of 88.

a) In proper notation, state the hypotheses of this test.

b) Show your calculation of the test statistic. ______ = ______________

c) Give the p-value of the test to 4 decimals. p = ________________________

d) What approach should the marketing executives take in light of the test result -- and why? That is, should they continue to base the sales campaign on an appeal to personal power or should they take a more sensitive approach along the lines of, say, " use your Enviroraptor to end world hunger"?

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-2.02

c) Give the p-value of the test to 4 decimals.

P-value = 0.0217

d) What approach should the marketing executives take in light of the test result -- and why? That is, should they continue to base the sales campaign on an appeal to personal power or should they take a more sensitive approach along the lines of, say, "use your Enviroraptor to end world hunger"?

Based on this test alone, the hypothesis that the average score on the Pearson Self-Absorption Test is at least 92 is not contradicted at the .02 level of significance. However perhaps they should consider that the p-value of the test is quite small, and had they chosen a significance level of .05 or even .03, the null hypothesis would have been rejected.

Solution:

This is an example of a hypothesis test for a population mean , where the population standard ...