Reading And Comprehension Questions For Chapter 9

Reading and Comprehension Questions for Chapter 9

1. This is a correct statement of a statistical hypothesis: H0 : 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

3. A type II error occurs if we fail to reject the null hypothesis when it is false.

True False

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

6. The power of a statistical test is 1 – Probability(type II error).

True False

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: H0:m= 10, H 0 : m 10. A 95% CI on the mean is 11＃m 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: H0:m= 10, H 0 : m > 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＃m 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＃m 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 H0:m= 10, H 0 : m 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

Sample Difference Size Power 2 10 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

H0:m= 10, H 0 : m 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 H0:m= 10, H 0 : m > 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, t 0.025,14 = 2.148, and t 0.01,14 = 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

20. Tests of hypothesis on a proportion use the normal approximation to the binomial distribution.

True False

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

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

24. Nonparametric or distribution-free statistical procedures make no assumptions about the form of the underlying distribution other than it is continuous.

True False

25. The sign test is used to test hypotheses about the median of a continuous distribution.

True False