Q1. A prison psychologist recorded the number of rule infractions for 15 prison inmates over a six-month period to be 5, 4, 2, 4, 3, 5, 2, 0, 4, 4, 5, 5, 3, 4, and 3.
a. Make a frequency table.
b. Make a histogram based on the frequency table.
c. Describe in words the shape of the histogram.
Q2. Identify and solve this problem by hand.
The head of public safety notices that the average driving speed at a particular intersection averages μ = 35 mph with a standard deviation of σ = 7.5 mph. After a school speed limit sign of 20 mph is placed at the intersection, the first 40 cars travel past at an average speed of 32 mph. Using the .01 significance level, was there a significant change in driving speed?
which under the null hypothesis follows a standard normal distribution.
Critical region: Reject H0 iff the absolute value of the test statistic is greater than 2.57583 ( point on a standard normal distribution above which 0.5% of the distribution lies)
Conclusion: Null hypothesis is accepted at 1% level of significance.
a. Sketch the distributions involved.
b. Figure the confidence limits for the 99% confidence interval.
Q3. A social psychologist gave a questionnaire about concern for farm workers to seven participants before and after they attended a film about union organization of farm workers. The results are shown below with high scores meaning high concern. Using the .05 significance level, do these results support the hypothesis that the film affected concern for the lives of farm workers?
Scores on the Concern Measure
Participant Before After
H0:
H1:
Mean before=10.714
Mean after =11
Standard deviation before=3.4017
Standard deviation after=5.774
Z==0.0825
Z-tabulated for two sided=1.96
Since 1.96>0.0825 we accept null hypothesis and conclude that film does not affect concern for the life of farm workers
b. Figure the effect size and find the approximate power of this study.
Q4. A team of cognitive psychologists studying the effects of sleep deprivation on short-term memory decay had eight participants stay in a sleep lab for two days. Four participants were randomly assigned to a condition in which they were not permitted to sleep during that period, while the other four participants were allowed to sleep when they wanted to. At the end of the two days, the participants completed a short-term memory task that yielded the results in the table that follows. Using the .05 significance level, did sleep deprivation reduce short-term memory?
Mean Number of Letters Remembered
Sleep Deprived Normal Sleep
7 9
8 8
7 11
9 7
a. Create the appropriate graph for this problem.
b. Use the five steps of hypothesis testing.
c. Figure the effect size.
d. From the hypothesis testing results, we conclude that there was no effect of sleep deprivation on short memory. There was no significant difference on the effects of the two, both the normal sleep and the ones who were deprived of sleep. The mean number of letters remembered for those who were deprived of sleep was 7.75 while as the mean for those with normal sleep was 8.75.