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 are shown below.
Use a 10% 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.
Ho
: Distributions are different.H1
: Distributions are the same.Ho
: Distributions are the same.H1
: Distributions are different.Ho
: Distributions are different.H1
: Distributions are different.Ho
: Distributions are the same.H1
: Distributions are the same.
(b) Compute the sample test statistic. (Use 2 decimal places.)
What sampling distribution will you use?
chi-squareuniform normalStudent'st
What conditions are necessary to use this distributions?
At least one sample size must be less than 10.Both sample sizes must be greater than 10. Both sample sizes must be less than 10.At least one sample size must be greater than 10.
(c) Find the
P-value of the sample test statistic. (Use 4 decimal places.)
(d) Conclude the test?
At the ? = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
(e) Interpret your conclusion in the context of the application.
Fail to reject the null hypothesis, there is sufficient evidence that alertness score distributions differ by lunch type.Fail to reject the null hypothesis, there is insufficient evidence that alertness score distributions differ by lunch type. Reject the null hypothesis, there is sufficient evidence that alertness score distributions differ by lunch type.Reject the null hypothesis, there is insufficient evidence that alertness score distributions differ by lunch type.