Hypothesis Testing & Regression Analysis

1. An obstetrician wants to learn whether the amount of prenatal care and the wantedness of the pregnancy are assoicated. He randomly selects 939 women who had recently given birth and asks them to disclose whether their pregnancy was intended, unintended, or mistimed. In addition, they were to disclose when they started receiving prenatal care, if ever. The results of the survey are as follows:

Less Than 3 Months 3 to 5 months More than 5 months (or never)
Intended 593 26 33
Unintended 64 8 11
Mistimed 169 19 16

Test whether prenatal care and the wantedness of pregnancy are independent at the 0.05 level of significance.

2. In an experiment conducted online at the University of Mississippi, study participants are asked to react to a stimulus. In one experiment, the participant must press a key on seeing a blue screen. Reaction time (in seconds) to press the key is measured. The same person is then asked to press a key on seeing a red screen, again with reaction time measured. The results for six randomly sampled study participants are as follows.

Participant 1 2 3 4 5 6
Blue 0.582 0.481 0.841 0.267 0.685 0.450
Red 0.408 0.407 0.542 0.402 0.456 0.533

Is the reaction time to the blue stimulus different from the reaction time to the red stimulus at the 0.01 level of significance?

3. Researchers conducted a randomized double-blind study to measure the effects of the drug olanzapine on patients diagnosed with bipolar disorder. A total of 115 patients with a DSM-IV diagnosis of bipolar disorder were randomly divided into two groups. The Experimental Group received 5 to 20 mg per day of olanzapine, while the Control Group received a placebo. The effectiveness of the drug was measured using the Young-Mania rating scale total score with the net improvement in the score reported. The results are presented in the table below. Does the evidence suggest that the experimental group experienced a larger mean improvement than the control group at the 0.01 level of significance?

Experimental Group Control Group
n 55 60
Mean Improvement 14.8 8.1
Sample Standard Deviation 12.5 12.7

4. The Pew Research Group conducted a poll in which they asked, "Are you in favor of, or opposed to, executing persons as a general policy when the crime was committed while under the age of 18?" Of the 580 Catholics surveyed, 180 indicated they favored capital punishment; of the 600 seculars surveyed, 238 favored capital punishment. Is there a significant difference in the proportion of individuals in these groups in favor of capital punishment for persons under the age of 18? Use a 0.01 level of significance.

5. Find the equation of the least squares regression line for the data below and use it to predict the value of y when x is 10.

x 3 5 7 9 11
y 0 2 3 6 9