A professor is interested in determining if attending college influences the level at which an individual cooperates with the police. The professor is unsure if attending college will teach respect for authority and thus increase level of cooperation or if college will teach independent thinking and thus lead to deceased level of cooperation. To address this question, the professor gathers information from the students in an undergraduate course and calculates their propensity for cooperating with the police (higher number means higher level of cooperation) and compares it to the known mean and standard deviation of the general population.
a) Would the professor conduct a 1-tailed or 2-tailed hypothesis test? Explain why.
b) Use the information below to conduct a z-test using p=.05 as your alpha level. Make sure you complete all 5 steps and show your work/answers for each step.
Population:
Mean = 3.02
SD = 0.54
Sample:
Mean = 3.13
SD = 0.53
n = 86
c) Calculate a 95% confidence interval for the above sample.
This is the answer I came up with for the standard error: ( σ μ ) = σ / √ n = .53 / √ 86 = .53 / 9.27 = .057
Your standard error should be calculated under the null hypothesis. A sample size of 86 from a population with SD=0.54 will have a standard error of the mean of $\frac{0.54}{\sqrt{86}} = 0.0582$ You used the sampel SD, which is not correct if you are doing a Z-test, as opposed to a t-test. Now, you need to create a two-sided 95% CI using this value, which is $3.13 \pm 1.96(0.0582)$