Statistics Quiz 1 2015/4/2 系級 姓名 學號
Multiple choice questions (80%, 4% each) 1. A sample of 51 elements is selected to estimate a 95% confidence interval for the variance of the population. The chi-square values to be used for this interval estimation are a. -1.96 and 1.96 b. 32.357 and 71.420 c. 34.764 and 67.505 d. 12.8786 and 46.9630
2. Which of the following has a chi-square distribution? a. (n - 1)s2/S2 b. (n - 2)s2/S2 c. (n - 1)S/s d. (n - 1)S2/s2
3. The value of F.95 (0.95 refer to the right tail prob.) with 8 numerator and 9 denominator degrees of freedom is a. 3.2296 b. 3.3881 c. 0.3096 d. 0.2951
4. The sampling distribution of the ratio of two independent sample variances taken from normal populations with equal variances is a. an F distribution b. a chi-square distribution c. a t distribution d. a normal distribution
Question 5-6, refer to Exhibit 1:
We are interested in determining whether or not the variances of the sales at two music stores (A and B) are equal. A sample of 26 days of sales at store A has a sample standard deviation of 30 while a sample of 16 days of sales from store B has a sample standard deviation of 20.
5. Refer to Exhibit 1. The test statistic is a. 1.50 b. 0.67 c. 1.56 d. 2.25
6. Refer to Exhibit 1. The p-value for this test is a. between 0.05 and 0.10 b. between 0.10 and 0.2 c. between 0.2 and 0.3 d. None of these alternatives is correct.
7. We are interested in testing whether the variance of a population is significantly less than 1.44. The null hypothesis for this test is 2 a. Ho: 1.44 2 b. Ho: s 1.44
c. Ho: 1.20 2 d. Ho: 1.44
8. The random variable for a chi-square distribution may assume a. any value between -1 to 1 b. any value between - infinity to +infinity c. any negative value d. any non-negative value
9. In order not to violate the requirements necessary to use the chi-square distribution, each expected frequency in a goodness of fit test must be a. at least 5 b. at least 10 c. no more than 5 d. less than 2
Question 10-11, refer to Exhibit 2: Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification. Freshmen 83 Sophomores 68 Juniors 85 Seniors 64 We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year.
10. Refer to Exhibit 2. The calculated value for the test statistic equals a. 0.5444 b. 300 c. 1.6615 d. 6.6615
11. Refer to Exhibit 2. The p-value is a. less than .005 b. between .025 and 0.05 c. between .05 and 0.1 d. greater than 0.1
Question 12-13, refer to Exhibit 3: The table below gives beverage preferences for random samples of teens and adults. Teens Adults Total Coffee 50 200 250 Tea 100 150 250 Soft Drink 200 200 400 Other 50 50 100 400 600 1,000 We are asked to test for independence between age (adult and teen) and drink preferences.
12. Refer to Exhibit 3. With a .05 level of significance, the critical value for the test is a. 1.645 b. 7.815 c. 14.067 d. 15.507
13. Refer to Exhibit 3. The p-value is a. between .1 and .05 b. between .05 and .025 c. between .025 and .01 d. less than 0.005
Question 14-16, refer to Exhibit 4: It is believed that sales of books at a local bookstore follow a Poisson distribution. Below you are given information on the number of books sold during a sample of 15- minute intervals. Number of Books Frequency 0 2 1 3 2 12 3 16 4 19 5 20 6 18 7 16 8 9 9 5 120
14. Refer to Exhibit 4. What is the expected number of 5 books sold using a Poisson probability table. (rounded) a. 20 b. 21 c. 22 d. 23
15. Refer to Exhibit 3. If you divided the group as [0 or 1, 2, 3,…, 7, 8, 9 or more] (total 9 groups) .The test statistic is a. 1.388 b. 2.333 c. 3.127 d. 5.556
16. Refer to Exhibit 3 and Question 13. Let = .05. What is the conclusion? a. Reject the null hypothesis b. Do not reject the null hypothesis c. Need more information to state the hypotheses d. None of these alternatives is correct.
17. A goodness of fit test is always conducted as a a. lower-tail test b. upper-tail test c. middle test d. None of these alternatives is correct.
18. Are all employees equally prone to having accidents? To investigate this hypothesis, Parry (1985) looked at a light manufacturing plant and classified the accidents by type and by age of the employee. Accident Type Age Sprain Burn Cut Under 25 9 17 5 25 or over 61 13 12 A chi-square test gave a test-statistic of 20.78. If we test at =.05: a. There appears to be no association between accident type and age. b. The proportion of sprain, cuts and burns seems to be similar for both age classes. c. Accident type does not seem to be independent of age. d. There appears to be a 20.78% correlation between accident type and age.
19. Which of the following has an F distribution? a. (n - 1)S/s
b. S1/S2
c. (n - 1)S1/S2 d.
20. Doctors’ practices have been categorized as to being Urban, Rural, or Intermediate. The number of doctors who prescribed tetracycline to at least one patient under the age of 8 were recorded for each of these practice areas. The results are: Urban Intermediate Rural Tetracycline 95 74 31 No tetracycline 126 84 30 If the county type of practice and the use of tetracycline are independent, then the expected number of rural doctors who prescribe tetracycline is: a. 31.0 b. 27.7 c. 1.37 d. 51%
21. (6%) Write down the definition of chi-square, t, and F distributions.
22. (8%) Write down the steps to test if random numbers follow a uniform distribution, using the chi-square goodness-of-fit test. Say, suppose you are given 200 random numbers and you are asked to separate them into 10 groups. Also, if the test statistics is 15.6, then what is your conclusion? (Bonus: Calculate the p- value!)
23. (6%) In class we mentioned that the chi-square test is one of the frequently used methods and many tests are related (or equivalent) to this test. Suppose we tossed a coin 500 times and observed “Head” 210 times. We want to know if this is a fair coin with a significance level = 0.05. (a) Using the Z-test to check if p = 0.5. (b) Repeat (a) but use the chi-square instead.
1. (c) 2.