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STAT 307 (Fall 17) ± Sample Exam 2 x Time: 50 min Name: ______________________________________________________ x Show all your work to get full and/or partial credits. x Box or circle your final answer when applicable. 1. Answer below questions shortly: a) Why we never construct 100% confidence interval?

b) As sample size increases, the shape of t-distribution will converge to what distribution?

c) Why we can always compute p-value of t-test by using tcdf(|t-stat|,1000,df), regardless the direction of tail?

e) To compute required sample size, how we round the result to integer?

d) Compare with the independent two sample test, what is the statistical advantage of conducting a paired t-test?

2.We conduct a random sampling with n=10 for below four population (A) through (D) a) Underline (all that apply) the label of graph that look likely to have normally distributed X Xμ

b) Circle (all that apply) the label of graph that we can not assume t-distribution on t tt = /√n0

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3. Fill blanks: a) If I set the α = 1, my hypothesis test will have power = __________, and type I error rate = __________ b) If I set the α = 0, my hypothesis test will have power = __________, and type I error rate = __________ c) For α = 0.05, β = 0.3, the power should be __________.

4. Which of the following statements about the p-value is true? (circle all that apply) (a) The p-value is the probability that the null hypothesis is true. (b) The p-value is the probability that the alternative hypothesis is true. (c) We reject the null hypothesis when the p-value < alpha (d) We accept the alternative hypothesis when the p-value < alpha (e) The p-value is the probability of observing a test statistic (data) that is as, or more, extreme than the one observed under the assumption that null hypothesis is true. (f) The p-value is the probability of observing a test statistic (data) that is as, or more, extreme than the one observed under the assumption that alternative hypothesis is true. (g) The p-value is the fixed and unknown population parameter. (h) The p-value is the random and known sample statistic.

5. For each of the following scenarios, determine how the changes will affect the Width of the confidence interval. You may use each of the following options more than once or not at all: (A) Increase

(B) Decrease

(C) No change

(D)Cannot be determined

a) Holding everything else constant, increase the point estimate. Width: ______ b) Holding everything else constant, increase the sample size and decrease the confidence level. Width: ______ c) Holding everything else constant, increase the sample size and increase the confidence level. Width: ______ d) Holding everything else constant, increase the number of population data. Width: ______

6. Compute the power for hypothesis test: H0 : 𝜇  0 vs. H : 𝜇 > 0, with α = 0.05 and n = 30. Suppose we estimated that the true mean is μ = 5.1, and population standard deviation σ = 10.

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