Hypothesis test of one mean
1. A random sample of eight students participated in apsychological test of depth perception. Two markers, one labeled Aand the other B, were arranged at a fixed distance apart at the farend of the laboratory. One by one the students were asked to judgethe 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 meandistance is more than 2 feet
- State the null and alternative hypothesis.
- Give the p-value
- Give a conclusion for the hypothesis test.
- Find a 95% Confidence Interval.
- Write a conclusion for the confidence interval
Hypothesis test of two means
2. A random sample of non-English majors at a selected collegewas used in a study to see if the student retained more fromreading a 19th century level novel or by watching it inDVD form. Each student was assigned one novel to read and adifferent one to watch, and then they were given a hundred pointquiz on each novel. The test results are shown:
DVDÂ Â Â Â Â Â Â Â Â 90 82 85 9570 75 85
BOOKÂ Â Â Â Â Â 95 85 95 75 8595 84
Alpha = 0.05, can it be concluded that the DVDscores are less than the BOOK?
- State the null and alternative hypothesis.
- Give the p-value.
- Give a conclusion for the hypothesis test.
Hypothesis test of one proportion
3. The national average for the percentage of high schoolgraduates taking the SAT is 49%. A random sample of 300 high schoolgraduating 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 ofhigh school graduates who take the SAT in this area agree with thenational average?
- State the null and alternative hypothesis.
- Give the p-value.
- Give a conclusion for the hypothesis test.
- Find a 95% Confidence Interval.
- Write a conclusion for the confidence interval.
Hypothesis test of two proportions
4. The drug Prevnar is a vaccine meant to prevent certain typesof bacterial meningitis. It is typically administered to infantsstarting around two months old. In a randomized doubled-blindclinical trials of Prevnar, infants were randomly divided into twogroups. Group 1 received Prevnar while Group 2 received a controlvaccine. After the second dose, 137 of 452 subjects in group 1effect experienced drowsiness as a side effect. After the seconddose, 31 of 99 subjects in Group 2 experienced drowsiness as a sideeffect. Does the evidence suggest that there is a differentproportion between the groups at alpha =0.05 level ofsignificance?
(a) State the null and alternative hypothesis
(b) Give the p-value
(c) Give a conclusion for the hypothesis test.
