Reading and Comprehension Questions for Chapter 9
1. This is a correct statement of a statistical hypothesis: H 0 : x  10 .
True False
False – an hypothesis involves one or more parameters of a distribution, and the sample
mean is not a parameter.
2. A type I error occurs if the null hypothesis is rejected when it is actually true.
True False
True
3. A type II error occurs if we fail to reject the null hypothesis when it is false.
True False
True
4. The probability of type II error increases if the difference between the hypothesize
value of the parameter increases, assuming that the sample size and other parameters do
not change.
True False
False – the probability of type II error will decrease if the difference between the
hypothesized value of the parameter increases, assuming that the sample size and other
parameters do not change.
5. In testing a statistical hypothesis about the mean of a distributing, the probability of
type II error decreases if sample size increases, assuming that the true value of the mean
and other parameters do not change.
True False
True
6. The power of a statistical test is 1 – Probability(type II error).
True False
True
7. Rejecting a null hypothesis is always a weak conclusion.
True False
False - rejecting the null hypothesis is always a strong conclusion because we can control
the probability of incorrectly rejecting this hypothesis (type I error). See page 299.
8. The P-value is the smallest level of significance that would lead to rejection of the null
hypothesis.
True False
True – see page 300.
9. If the P-value for a certain hypothesis test is 0.0125, we can say that the null
hypothesis is rejected at the level of significance 0.01.
True False
False – the null hypothesis could be rejected at any level of significance greater tan or
equal to 0.0125. See Section 9-1.4.
10. Suppose that you are testing the following hypotheses: H 0 :   10, H 0 :   10. A
95% CI on the mean is 11    13 . Select the correct answer from the following:
a. The null hypothesis cannot be rejected at the five percent level of significance.
b. The null hypothesis can be rejected at the five percent level of significance.
c. The null hypothesis can be rejected at the one percent level of significance.
c. No conclusion about the null hypothesis can be drawn.
Answer – the correct choice is b. See section 9-1.5 page 301.
11. Statistical significance always implies practical significance.
True False
False – see page 302.
12. Suppose that you are testing the following hypotheses: H 0 :   10, H 0 :   10. If the
null hypothesis is rejected at the one percent level of significance, what statement can
you make about the CI on the mean?
a. 9    13
b. The lower bound of a 95% one-sided CI on the mean exceeds zero.
c. The lower bound of a 95% one-sided CI on the mean exceeds 10.
d. 10    15
e. No statement can be made.
Answer – b. The connection between CIs and hypothesis tests is discussed on page 301.
13. You are testing H 0 :   10, H 0 :   10 with known standard deviation. The sample
size is n = 15, the test statistic value is z0 = 2.45, and the P-value is 0.0143. If the value
of the test statistic had been 2.00 the P-value would have been larger.
True False
False – because the calculated value of the test statistic is smaller, the P-value must be
smaller. See page 308.
14. Suppose that you are testing a hypothesis on the mean of a normal distribution and
are interested in determining the appropriate sample size. Consider the following
display:
Power and Sample Size
1-Sample Z Test
Testing mean = null (versus not = null)
Calculating power for mean = null + difference
Alpha = 0.05 Assumed standard deviation = 3
Difference
2
Sample
Size
10
Power
0.558940
What would happen to the power of the test if the sample size was increased to 20?
a. Power would increase
b. Power would decrease
c. Power would not change
d. Results are not predictable
Answer – a. Power increases with an increase in sample size.
15. Consider the information in question 14. If the standard deviation were smaller than
3, the power would be larger.
True False
True – Remember that Power = 1 – Probability(type II error).
16. If the population standard deviation is unknown, the test statistic for
H 0 :   10, H 0 :   10 would be compared to the chi-square distribution.
True False
False – the test statistic is compared to the t-distribution.
17. You are testing H 0 :   10, H 0 :   10 with unknown standard deviation and a
sample size of n = 15. The computed value of the test statistic is t0 = 2.45. Because
t0.01,14  2.625 we can say that the null hypothesis can be rejected at the 0.01 level of
significance.
True False
False – t0 would have to exceed to 2.625 to reject the null hypothesis at the 0.01 level.
18. Reconsider question 17. Because t0.05,14  1.76, t0.025,14  2.148, and t0.01,14  2.625 we
can say that the P-value for this test is:
a. P > 0.05
b. 0.05 > P > 0.025
c. 0.025 > P > 0.01
Answer – c. The computed value of the test statistic is between the 0.025 and 0.01
percentage points of the t distribution.
19. Hypothesis tests on the variance of a normal distribution refer the test statistic to a
chi-square distribution.
True False
True
20. Tests of hypothesis on a proportion use the normal approximation to the binomial
distribution.
True False
True
21. A chi-square test for goodness-of-fit can be used instead of probability plotting to
determine if a particular distribution adequately describes the population from which a
sample was drawn.
True False
True
22. A contingency table is a tabular arrangement of data that have been classified
according to two criteria.
True False
True
23. A contingency table can be used to test for independence between the two variables
of classification when all of the observations are selected from a single population.
True False
True
24. Nonparametric or distribution-free statistical procedures make no assumptions about
the form of the underlying distribution other than it is continuous.
True False
True
25. The sign test is used to test hypotheses about the median of a continuous distribution.
True False
True