Discuss the below:
Q1. Find the expected values of the following probability distributions:
Yi PYi Yi PYi
5 .15 5 .20
10 .25 10 .30
15 .05 15 .15
20 .20 20 .30
25 .35 25 .05
Q2. In as population of test scores not known to be normally distributed, the mean is 50 and the standard deviation is 5. What proportion of the observations will fall in the interval from 40 to 60?
Q3. Using the central limit theorem, find the means and standard errors of sampling distributions with the following characteristics:
μ2y σ2y N
a. 10.5 50 25
b. 50 115 115
c. 25 75 250
d. 12 70 35
e. 100 100 200
Q4. Test the null hypothesis that μy = 75 for a sample of 25 subjects in which Y‾= 81 and sy = 10 for a one-tailed test in which α= .01. State (a) critical value; (b) degrees of freedom: (c) test statistic: and (d) your decision.
Q5. Test the null hypothesis that μy = 50 for a sample where N = 36, Y‾ =.17.5, and sy= 12 using a two-tailed test in which α= .001. State (a) critical value; (b) degrees of freedom; (c) test statistic: and (d) your decision.
Q6. After six months in office. a U.S. senator evaluates her public approval rating by surveying 50 citizens. Their responses indicate that the senator has a 63% mean approval rating, with a variance of 16. If 60% is the minimum approval rating the senator will accept in order to continue her current agenda. can she conclude that her approval rating is significantly above the minimum? Set α = .01.