A psychologist has developed a mental alertness test. She wishes to study the effects (if any) of type of food consumed on mental alertness. Twenty-one volunteers were randomly divided into two groups. Both groups were told to eat the amount they usually eat for lunch at noon. At 2:00 _P.M., all subjects were given the alertness test. Group A had a low-fat lunch with no red meat, lots of vegetables, carbohydrates, and fi­ber. Group B had a high-fat lunch with red meat, vegetable oils, and low fi­ber. The only drink for both groups was water. The test scores follow.

Use a 1% level of signifi­cance to test the claim that there is no difference in mental alertness distributions based on type of lunch.

(a) What is the level of signifi­cance? State the null and alternate hypotheses.

(b) Compute the sample test statistic. What is the sampling distribution?

What conditions are necessary to use this distribution?

(c) Find the P-value of the sample test statistic.

(d) Conclude the test.

(e) Interpret the conclusion in the context of the application.

Transcribed Image Text:

Group A76 93 52 81 68 79 88 90 67 85 60 Group B 44 57 60 91 62 86 82 65 96 42 68 98