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1. The t-distribution approaches the normal distribution as the number of degrees of freedom decreases. A) True B) False Answer: B) False 2. The sampling distribution of sample proportions p' is approximately distributed as a Student’s t-distribution. A) True B) False Answer: B) False 3. The chi-square distribution is used for inferences about the population mean µ when the standard deviation s is unknown. A) True B) False Answer: B) False 4. The chi-square distribution is a skewed distribution whose mean value is n for degrees of freedom larger than two. A) True B) False Answer: A)True 5. Independent samples are obtained by using unrelated sets of subjects. A) True B) False Answer: A) True 6. In dependent sampling, the two data values, one from each set, that come from the same source are called paired data. A) True B) False Answer: A) True 7. The z-distribution is used when two dependent means are to be compared. A) True B) False Answer: B) False 8. The standard normal score is used for all inferences concerning population proportions. A) True B) False Answer: A) True 9. Each F-distribution is identified by two numbers of degrees of freedom, one for each of the two samples involved. A) True B) False Answer: A) True 10. The chi-square distribution is used for making inferences about the ratio of the variances of two populations. A) True B) False Answer: B) False 11. In a two-tailed test, with n = 20, the computed value of t is found to be t* = 1.85. Assuming the sample is randomly selected from a normal population, then the p-value is given by: A) 0.005 < p-value < 0.01. B) 0.01 < p-value < 0.02. C) 0.025 < p-value < 0.05. D) 0.05 < p-value < 0.10. Answer: D) 0.05 < p-value < 0.10. 12. In comparing Student's t-distribution to the standard normal distribution, we see that Student's t-distribution is: A) less peaked and thinner at the tails. B) less peaked and thicker at the tails. C) more peaked and thinner at the tails. D) more peaked and thicker at the tails. Answer: B) less peaked and thicker at the tails. 13. Which of the following would be the hypothesis for testing the claim that the proportion of students at a large university who smoke is significantly different from 0.15? A) H o: p = 0.15(=), H a: p > 0.15 B) H o: p = 0.15, H a: p ? 0.15 C) H o: p > 0.15, H a: p = 0.15 D) H o: p < 0.15, H a: p > 0.15 Answer: B) B) H o: p = 0.15, H a: p ≠ 0.15. 14. As the binomial parameter p gets larger, then q A) gets smaller. B) also gets larger. C) stays the same. D) size depends on n. Answer: A) gets smaller. 15. The mean age of 25 randomly selected college seniors was found to be 23.5 years, and the standard deviation of all college seniors was 1.3 years. The correct symbol for the 1.3 years is which of the following? A) µ B) s C) σ D) x Answer: C) σ (Sigma) 16. In a chi-square distribution, the mean is equal to the A) degrees of freedom. B) median. C) mode. D) standard deviation. Answer: A) degrees of freedom 17. Which of the following critical values of the chi-square distribution is the largest? A) ? 2 (20,0.025) B) ? 2(12,0.95) C) ? 2(8, 0.005) D) ? 2 (15,0.90) Answer: A) Chi-2 (20,0.025) 18. Studies that involve paired subjects deal with A) dating service samples. B) independent samples. C) dependent samples. D) None of the above. Answer: C) dependent samples. 19. You plan to test the dependent sampling claim: “a particular weight loss program is effective in weight reduction.” What would be the null hypothesis, if d=X after -X before? A) Ho: µd = 0 B) Ho: µd = 0 (=) C) Ho: µd ? 0 D) Ho: µd = 0 (=) Answer: B) Ho: µd = 0 (=) greater than or equal to Ho: μd ≥ 0 (null hypothesis) Ha: μd < 0 (alternative hypothesis) 20. If two independent samples are used in a hypothesis test concerning the difference between population means for which the combined degrees of freedom is 20, which of the following could not be true about the sample sizes n1 and n2? A) n1=12 and n2=8 B) n1=12 and n2=10 C) n1=13 and n2=9 D) Cannot be determined from the given information Answer: A) n1=12 and n2=8 21. To test the null hypothesis that the mean waist size for males under 40 years equals 34 inches versus the hypothesis that the mean differs from 34, the following data were collected: 33, 33, 30, 34, 34, 40, 35, 35, 32, 38, 34, 32, 35, 32, 32, 34, 36, 30. Calculate the t* -value of the test statistic. From the given data, xbar = 33.83, s = 2.526, n =18 Thus the test statistic t = (xbar - μ)/(s/sqrt(n)) = (33.83 - 34)/(2.526/sqrt(18)) = -0.286 22. State the null hypothesis, Ho,and the alternative hypothesis, Ha , that would be used to test the claim: The standard deviation has increased from its previous value of 15. Ho: σ ≤ 15 Ha: σ > 15 23. A particular candidate claims she has the support of at least 60% of the voters in her district. A random sample of 150 voters yields 87 who support her. The candidate wishes to test her claim at the 0.05 level of significance. Compute the value of test statistic. Here it is given that, p-bar = 87/150 = 0.58, p=0.60, n =150 The test statistic is z= (0.58 - 0.60)/Sqrt((0.60(1-0.60)/150)) = -0.5 24. A random sample of 51 observations was selected from a normally distributed population. The sample mean was x = 88.6 , and the sample variance was s2 = 38.2. We wish to determine if there is sufficient reason to conclude that the population standard deviation is not equal to 8 at the 0.05 level of significance. Calculate the value of the test statistic. The test statistics is X^2 = (n-1)s^2/σ^2 = (51-1)38.2/8^2 = 29.84 25. Consider testing Ho: µd = 0 vs. Ha: µd = > 0 with n =20 and t* =1.95. Place bounds on the p-value using the table of “critical values of Student’s t-distribution” available in your textbook. 0.01 < p-value < 0.05 26. Consider the following paired data. A 5 B 2 4 1 3 5 4 1 4 3 Calculate Sd , Sd 2 , d(bar), and sd . d=A-B : 3, 3, -2, 0, -2 Σd = 3 + 3 - 2 + 0 - 2 = 2 Σd 2 = 3^2 + 3^2 + (-2)^2 + 0 + (-2)^2 = 26 dbar = (Σd)/n = (3 + 3 - 2 + 0 - 2)/5 = 0.4 sd = Square root[ Σd 2 - (Σd )^2/n ] = Square root(26 - 2^2/5) = 5.02 27. A group of sheep, infested with tapeworms, are randomly divided into two groups as follows. Each sheep is assigned a number (1 through 20) and then 10 numbers are selected by drawing 10 slips of paper from a box having the numbers 1 through 20 written on them. The drawing divides the sheep into two groups. One group is given a placebo and the other is given an experimental drug. After six weeks the sheep are sacrificed and tapeworm counts are made. Do these samples represent dependent or independent samples? Answer: Independent samples