An article in Marketing News (T. T. Semon, “Consider
a Statistical Insignificance Test,” Marketing News,
February 1, 1999) argued that the level of significance used
when comparing two products is often too low—that is,
sometimes you should be using an value greater than 0.05.
Specifically, the article recounted testing the proportion of
potential customers with a preference for product 1 over
product 2. The null hypothesis was that the population proportion
of potential customers preferring product 1 was
0.50, and the alternative hypothesis was that it was not equal
to 0.50. The p-value for the test was 0.22. The article suggested
that, in some cases, this should be enough evidence
to reject the null hypothesis.
a. State, in statistical terms, the null and alternative
hypotheses for this example.
b. Explain the risks associated with Type I and Type II
errors in this case.
c. What would be the consequences if you rejected the null
hypothesis for a p-value of 0.22?
d. Why do you think the article suggested raising the value
of a ?
e. What would you do in this situation?
f. What is your answer in (e) if the p-value equals 0.12?
What if it equals 0.06?
This question was answered on: Sep 21, 2023
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