DISCUSSION 5
In the following multiple-choice questions, please indicate the correct answer.
1. In order to determine the p-value, which of the following is not needed? a. The level of significance b. Whether the test is one or two tail c. The value of the test statistic d. All of the above are needed
2. In testing the hypotheses
H 0 : 50
H1 : 50 the following information is known: n = 64, x = 53.5, and = 10. The standardized test statistic equals: a. 1.96 b. –2.8 c. 2.8 d. –1.96
3. If a hypothesis is not rejected at the 0.10 level of significance, it: a. must be rejected at the 0.05 level b. may be rejected at the 0.05 level c. will not be rejected at the 0.05 level d. must be rejected at the 0.025 level
4. In testing the hypothesis
H 0 : 75 H1 : < 75 if the value of the test statistic equals –2.42, then the p-value is: a. 0.5078 b. 2.420 c. 0.9922 d. 0.0078
5. For a two-tail test, the null hypothesis will be rejected at the 0.05 level of significance if the value of the standardized test statistic is: a. smaller 1.96 b. greater than –1.96 c. smaller than –1.96 d. smaller than 1.645
6. In testing the hypothesis
H 0 : 800
H1 : 800 if the value of the test statistic equals 1.75, then the p-value is: a. 0.0401 b. 0.0802 c. 0.4599 d. 0.9198
7. A Type I error is committed if we make: a. a correct decision when the null hypothesis is false b. correct decision when the null hypothesis is true c. incorrect decision when the null hypothesis is false d. incorrect decision when the null hypothesis is true
8. Which of the following p-values will lead us to reject the null hypothesis if the level of significance equals 0.05? a. 0.15 b. 0.10 c. 0.5 d. 0.025
9. A professor of statistics refutes the claim that the average student spends 3 hours studying for the midterm exam. Which hypothesis is used to test the claim?
a. H 0 : 3
H1 : 3
b. H 0 : 3
H1 : 3
c. H 0 : 3
H1 : 3
d. H 0 : 3
H1 : 3
10. Suppose that we reject a null hypothesis at the 0.05 level of significance. Then for which of the following -values do we also reject the null hypothesis? a. 0.06 b. 0.04 c. 0.03 d. 0.02
11. In hypothesis testing, whatever we are investigating or researching is specified as: a. the null hypothesis b. the alternative hypothesis c. either the null or alternative d. the p-value
12. In a two-tail test for the population mean, the null hypothesis will be rejected at level of significance if the value of the standardized test statistic z is such that:
a. z > z
b. z < -z
c. -z < z < z
d. |z| > z / 2
13. Statisticians can translate p-values into several descriptive terms. Which of the following statements is correct? a. If p-value < 0.01, there is overwhelming evidence to infer that the alternative hypothesis is true b. If 0.01 < p-value < 0.05, there is strong evidence to infer that the alternative hypothesis is true c. If 0.05 < p-value < 0.10, there is weak evidence to infer that the alternative hypothesis is true d. All of the above statements are correct
14. A spouse stated that the average amount of money spent on Christmas gifts for immediate family members is above $1200. The correct set of hypotheses is:
a. H 0 : 200
H1 : 1200
b. H 0 : 1200
H1 : 1200
c. H 0 : 1200
H1 : 1200
d. H 0 : 1200
H1 : 1200
15. The probability of a Type I error is denoted by: a. b. 1- c. d. 1-
16. If we reject the null hypothesis, we conclude that : a. there is enough statistical evidence to infer that the alternative hypothesis is true b. there is not enough statistical evidence to infer that the alternative hypothesis is true c. there is enough statistical evidence to infer that the null hypothesis is true d. the test is statistically insignificant at whatever level of significance the test was conducted at
17. In a given hypothesis test, the null hypothesis can be rejected at the .10 and .05 level of significance, but cannot be rejected at the .01 level. The most accurate statement about the p-value for this test is: a. p-value = 0.01 b. p-value = 0.10 c. 0.01 < p-value < 0.05 d. 0.05 < p-value < 0.10
18. In a one-tail test, the p-value is found to be equal to 0.068. If the test had been two-tail, the p-value would have been: a. 0.932 b. 0.466 c. 0.034 d. 0.136
19. The rejection region for testing
H 0 : 100
H1 : 100 at the 0.05 level of significance is: a. |z| < 0.95 b. |z| > 1.96 c. z > 1.65 d. z < 2.33
20. The rejection region for testing
H 0 : 80
H1 : < 80 at the 0.10 level of significance is: a. z > 1.96 b. z < 0.90 c. z > -1.65 d. z < -1.28
21. The p-value criterion for hypothesis testing is to reject the null hypothesis if: a. p-value = b. p-value < c. p-value > d. - < p-value <
22. The use of the standard normal distribution for constructing confidence interval estimate for the population proportion p requires: a. npˆ and n(1 pˆ ) are both greater than 5, where pˆ denotes the sample proportion b. np and n(1-p) are both greater than 5 c. n(p+ pˆ ) and n(p- pˆ ) are both greater than 5 d. that the sample size is greater than 5
23. Based on sample data, the 90% confidence interval limits for the population mean are
LCL = 170.86 UCL = 195.42.
If the 10% level of significance were used in testing the hypotheses
H 0 : 201
H1 : 201, the null hypothesis: a. would be rejected b. would not be rejected c. would have to be revised d. None of the above
24. The Student t distribution approaches the normal distribution as the: a. degrees of freedom increase b. degrees of freedom decrease c. sample size decreases d. population size increases
25. Which of the following is true about the t distribution? a. Approaches the normal distribution as its degrees of freedom increase b. Assumes the population is normally distributed c. It is more spread out than the standard normal distribution d. All of the above statements are true
26. For each of the following pairs of null and alternative hypotheses, determine whether or not the pair would be appropriate for testing a hypothesis.
a. H 0 : 25
H1 : 25
b. H 0 : 30
H1 : 30
c. H 0 : x 35
H1 : x 35
d. H 0 : x 40
H1 : x 40
e. H 0 : 50
H1 : 50
27. For each of the following statements, formulate appropriate null and alternative hypotheses and indicate whether the appropriate test will be one-tail or two-tail.
a. The average TOEFL score for international students is well above 575. b. The average American adult drinks less than 3 cups of coffee per day c. The average housewife works more than 40 hours per week in house related activities. d. The average employee calls in sick is different from 3 times a year.