A study is done to evaluate the readability of a pamphlet that is being develope

Question

A study is done to evaluate the readability of a pamphlet that is being developed as part of an addictions awareness campaign. People over the age of ten are able to comprehend 75% of an earlier version’s content, on average. The goal of this study is to compare the readability of the new version to the previous version. After reading the new version of the pamphlet, a representative group of study participants complete a test scored out of 100 to assess their comprehension of the information in the new version. Based on the test scores (x-bar = 73.6), a p-value of 0.12 is computed for the test of H0: = 75 versus Ha: 75.

a. The following interpretation of this P-value is INCORRECT: There is a 0.12 probability that the true mean score on a comprehension test completed by people over ten years of age after they read the new version of the pamphlet is 75. Explain why this interpretation is incorrect.

b. What is the correct interpretation of this P-value?

c. Be sure to write your conclusion in terms of the context of this study. Write a conclusion for this hypothesis test in the context of the study.

Explanation / Answer

(a)

The p-value give the probability of getting results as our sample statistics under the assumption that null hypothesis true.

Incorrect : The given statement said that 0.12 is the probability of getting true mean score which is wrong.

b)

There is a 0.12 probability that of getting these sample results under the assumption that the true mean score on a comprehension test completed by people over ten years of age after they read earlier version’s content of the pamphlet is 75.

c)

Since p-value is greater than 0.05 so we fail to reject the null hypothesis. That is we can conclude that People over the age of ten are able to comprehend 75% of an new version’s content, on average.

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