1) Assuming two equally matched teams and independent outcomes, we showed in Handout 12 that,
theoretically, the probability that the World Series will last exactly 7 games is .3125. Out of 93 World
Series actually played, 34 lasted 7 games. The p-value obtained in a hypothesis test (with a two-sided
alternative) that the theory is correct is:
A) .2714
B) .1357
C) .7286
D) .8643
E) None of the Above.
Answer: A
2) Suppose we wish to test
H 0 :   0 versus H A :    0 . A large sample yields a t-statistic of 2.4.
Compute the p-value for this situation.
A) .4918
B) .0082
C) .0164
D) .9918
E) None of the Above.
Answer: C
3) In testing
H 0 :   0 versus H A :    0 . based on a sample of size 500, we obtain a p-value of .5,
based on the t-statistic. Suppose that the sample standard deviation was 2.1, and that
the sample mean, x , was:
A) 0
B) 1
C) 2.1 D) –1
 0  0. The value of
E) None of the Above.
Answer: A
4) Consider the following statement: “The larger the p-value, the higher the probability that the alternative
hypothesis is true.” If this statement is correct, explain why. If this statement is not correct, explain why
and then provide a correct statement starting with “The larger the p-value …”.
Answer: The statement is incorrect. Since there is nothing random about the null hypothesis, we cannot talk
about the probability that it is true. (We also cannot talk about the probability that the alternative hypothesis
is true). A correct statement would be: “The larger the p-value, the weaker the evidence against the null
hypothesis”. We could also say: “The larger the p-value, the weaker the evidence in favor of the alternative
hypothesis”.
5) Suppose we wish to test
H 0 :   0 versus H A :    0 at level .05 using a t-test based on a
sample of size n=15. The rejection region for this test is:
A) |t|>1.753
B) |t|>2.131
C) |t|>1.761
D) |t|>2.145
E) None of the Above
Answer: D
6) For a given data set, if the 95% confidence interval for  is (.004, .396) and the 99% confidence interval
for  is (.0576, .4576), then at which significance level(s) can the null hypothesis H 0 :   0 be
rejected in favor of the alternative hypothesis H A :   0 ?
A) .01 but not .05
B) .05 and .01
C) .05 but not .01
E) It cannot be determined
Answer: C
D) Neither .05 nor .01
7) Suppose we have two random samples from a population (with an unknown population mean  and
unknown population standard deviation), of sizes n=10 and n=15. Let’s call them “Sample 1” and “Sample
2”, respectively. True or false: The 95% confidence interval for  based on Sample 1 must be wider than
the 95% confidence interval for  based on Sample 2.
A) True
B) False.
Answer: False
8) Consider a test of
H 0 :   1 versus H A :   1 at level .05 using a t-test based on a sample of size
n=10. Suppose that the t-statistic is positive and falls exactly on the border of the rejection region. Suppose
also that the sample mean is 2. Then the value of the sample standard deviation is:
A) 1.398
B) .4421
C) 1.725
D) 1.613
E) None of the Above
Answer: A
9) A random sample of size 11 from a normal population yields a sample mean of 2.4 and a sample
standard deviation of 3.6. The 95% confidence interval for the population mean is:
A) (.4332 , 4.367)
B) (.0109 , 4.789)
C) (.2725 , 4.527)
D) (.0184 , 4.818)
E) None of the Above.
Answer: D
10) Suppose that someone tries to predict the outcome (Heads or tails) for 20 tosses of a coin, and succeeds
12 times. Based on this data, compute a 95% confidence interval for their probability of making a correct
prediction.
A) (.3178, .8822)
B) (.3853, .8147)
C) (.4198, .7802)
D) (.3452, .8548)
E) None of the Above.
Answer: B
11) Here is a new way to do a hypothesis test of
H 0 :    0 versus H A :    0 based on a sample of
size 200. First, split data set into two halves (100 data points each), selected at random. For each of the two
halves, construct the p-value appropriate for this test, in the usual way. Then, reject H 0 if either (or both)
of the two p-values is less than .05. What is the actual significance level of this test?
A) .10
B) .025
C) .05
D) .0975
E) None of the Above
Answer: Assume that the null hypothesis is true. The significance level is Prob{Reject the Null
Hypothesis}=Prob{First p-value is less than .05 or Second p-value is less than .05}. Since the two samples
are independent of each other, so are the two p-values, so the significance level becomes Prob{(First pvalue is less than .05)  (Second p-value is less than .05)}= .05 + .05  (.05)(.05) = .0975. Answer is D.