Question

Hypothesis test of one mean

1. A random sample of eight students participated in a psychological test of depth perception. Two markers, one labeled A and the other B, were arranged at a fixed distance apart at the far end of the laboratory. One by one the students were asked to judge the distance between the two markers at the other end of the room. The sample data (in feet) were as follows:

2.2, 2.3, 2.7, 2.4, 1.9, 2.4, 2.5, 2.6

At the alpha =0.05 level of significance, test if the mean distance is more than 2 feet

1. State the null and alternative hypothesis.
2. Give the p-value
3. Give a conclusion for the hypothesis test.
4. Find a 95% Confidence Interval.
5. Write a conclusion for the confidence interval

Hypothesis test of two means

2. A random sample of non-English majors at a selected college was used in a study to see if the student retained more from reading a 19^th century level novel or by watching it in DVD form. Each student was assigned one novel to read and a different one to watch, and then they were given a hundred point quiz on each novel. The test results are shown:

DVD          90 82 85 95 70 75 85

BOOK       95 85 95 75 85 95 84

Alpha = 0.05, can it be concluded that the DVD scores are less than the BOOK?

1. State the null and alternative hypothesis.
2. Give the p-value.
3. Give a conclusion for the hypothesis test.

Hypothesis test of one proportion

3. The national average for the percentage of high school graduates taking the SAT is 49%. A random sample of 300 high school graduating seniors were polled across a particular tri state area, and it was found that 195 had taken the SAT.

At alpha = 0.05 level of significance, does the proportion of high school graduates who take the SAT in this area agree with the national average?

1. State the null and alternative hypothesis.
2. Give the p-value.
3. Give a conclusion for the hypothesis test.
4. Find a 95% Confidence Interval.
5. Write a conclusion for the confidence interval.

Hypothesis test of two proportions

4. The drug Prevnar is a vaccine meant to prevent certain types of bacterial meningitis. It is typically administered to infants starting around two months old. In a randomized doubled-blind clinical trials of Prevnar, infants were randomly divided into two groups. Group 1 received Prevnar while Group 2 received a control vaccine. After the second dose, 137 of 452 subjects in group 1 effect experienced drowsiness as a side effect. After the second dose, 31 of 99 subjects in Group 2 experienced drowsiness as a side effect. Does the evidence suggest that there is a different proportion between the groups at alpha =0.05 level of significance?

(a) State the null and alternative hypothesis

(b) Give the p-value

(c) Give a conclusion for the hypothesis test.

Answer 1