EXAM 3 Math 1342 Elementary Statistics 6-7

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1 EXAM 3 Math 1342 Elementary Statistics 6-7 Name Date ********************************************************************************************************************************************** MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) Find the critical value zc that corresponds to a 95% confidence level. A) ±2.575 B) ±1.645 C) ±2.33 D ±1.96 1) 2) A random sample of 120 students has a test score average with a standard deviation of 9.2. Find the margin of error if c = A) 0.82 B) 0.18 C) 1.96 D ) 3) A random sample of 150 students has a grade point average with a mean of 2.86 and with a standard deviation of Construct the confidence interval for the population mean, μ, if c = A) (2.31, 3.88) B) (2.51, 3.53) C) (2.43, 3.79) D (2.71, 3.01) 3) 4) A nurse at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she desires to be 99% confident that the true mean is within 2 ounces of the sample mean? The standard deviation of the birth weights is known to be 7 ounces. A) 81 B) 82 C) 9 D 10 4) 5) Find the critical value, tc, for c = 0.90 and n = 15. A) B) C) D ) 6) Find the value of E, the margin of error, for c = 0.99, n = 10 and s = 3.2. A) 3.21 B) 3.29 C) 2.85 D ) 7) Find the value of E, the margin of error, for c = 0.95, n = 15 and s = 5.2. A) 2.36 B) 0.74 C) 2.96 D ) A-1

2 8) When 435 college students were surveyed,120 said they own their car. Find a point estimate for p, the population proportion of students who own their cars. A) B) C) D ) 9) In a survey of 2480 golfers, 15% said they were left-handed. The survey's margin of error was 3%. Construct a confidence interval for the proportion of left-handed golfers. A) (0.12, 0.18) B) (0.11, 0.19) C) (0.12, 0.15) D (0.18, 0.21) 9) 10) A manufacturer of golf equipment wishes to estimate the number of left-handed golfers. How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 2%? A previous study indicates that the proportion of left-handed golfers is 8%. A) 707 B) 1086 C) 999 D 17 10) 11) Find the critical values, X 2 R and X 2 L, for c = 0.95 and n = ) A) and B) and C) and D and Assume the sample is taken from a normally distributed population and construct the indicated confidence interval. 12) The mean replacement time for a random sample of 12 microwave ovens is 8.6 years with a 12) standard deviation of 4.2 years. Construct the 98% confidence interval for the population variance, σ2. A) (7.8, 63.6) B) (7.4, 54.3) C) (1.9, 15.1) D (2.8, 8.0) 13) The stem-and-leaf plot shows the test scores of 16 randomly selected students. Construct a 99% confidence interval for the population standard deviation. 13) A) (7.61, 20.33) B) (57.97, ) C) (7.89, 19.07) D (62.18, ) A-2

3 Provide an appropriate response. 14) Given H0: p 80% and Ha: p < 80%, determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. A) two-tailed B) left-tailed C) right-tailed 14) 15) Given H0: μ 25 and Ha: μ > 25, determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. A) two-tailed B) right-tailed C) left-tailed 15) 16) A researcher claims that 62% of voters favor gun control. Determine whether the hypothesis test for this claim is left-tailed, right-tailed, or two-tailed. A) two-tailed B) right-tailed C) left-tailed 16) 17) The mean age of bus drivers in Chicago is 50.2 years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis? A) There is sufficient evidence to support the claim μ = B) There is not sufficient evidence to reject the claim μ = C) There is sufficient evidence to reject the claim μ = D There is not sufficient evidence to support the claim μ = ) 18) The mean age of bus drivers in Chicago is 59.3 years. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis? A) There is sufficient evidence to reject the claim μ = B) There is sufficient evidence to support the claim μ = C) There is not sufficient evidence to reject the claim μ = D There is not sufficient evidence to support the claim μ = ) 19) Given H0: μ 12, for which confidence interval should you reject H0? A) (13, 16) B) (10, 13) C) (11.5, 12.5) 19) 20) Suppose you are using α = 0.05 to test the claim that μ > 14 using a P-value. You are given the sample statistics n = 50, x = 14.3, and s = 1.2. Find the P-value. A) B) C) D ) A-3

4 21) Given H0: μ = 25, Ha: μ 25, and P = Do you reject or fail to reject H0 at the 0.01 level of significance? A) not sufficient information to decide B) fail to reject H0 C) reject H0 21) 22) Find the critical value for a right-tailed test with α = 0.01 and n = 75. A) B) 2.33 C) 1.96 D ) 23) You wish to test the claim that μ > 32 at a level of significance of α = 0.05 and are given sample statistics n = 50, x = 32.3, and s = 1.2. Compute the value of the standardized test statistic. Round your answer to two decimal places. A) 3.11 B) 0.98 C) 1.77 D ) 24) You wish to test the claim that μ 38 at a level of significance of α = 0.01 and are given sample statistics n = 40, x = 39.8, and s = 4.3. Compute the value of the standardized test statistic. Round your answer to two decimal places. A) 2.12 B) 3.51 C) 1.96 D ) 25) You wish to test the claim that μ = 1240 at a level of significance of α = 0.01 and are given sample statistics n = 35, x = 1210 and s = 82. Compute the value of the standardized test statistic. Round your answer to two decimal places. A) B) C) D ) 26) Suppose you want to test the claim that μ 3.5. Given a sample size of n = 47 and a level of significance of α = 0.10, when should you reject H0? A) Reject H0 if the standardized test statistic is greater than or less than B) Reject H0 if the standardized test statistic is greater than or less than C) Reject H0 if the standardized test statistic is greater than 1.96 or less than D Reject H0 if the standardized test statistic is greater than 2.33 or less than ) 27) Find the critical values for a sample with n = 15 and α = 0.05 if H0: μ 20. A) B) C) D ) A-4

5 28) Find the standardized test statistic t for a sample with n = 12, x = 22.2, s = 2.2, and α = 0.01 if H0: μ = 21. Round your answer to three decimal places. A) B) C) D ) 29) Determine whether the normal sampling distribution can be used. The claim is p < 0.25 and the sample size is n = 18. A) Use the normal distribution. B) Do not use the normal distribution. 29) 30) Find the critical X2 -values to test the claim σ2 = 4.3 if n = 12 and α = A) 4.575, B) 3.053, C) 3.816, D 2.603, ) 31) Find the critical X2 -value to test the claim σ2 1.8 if n = 15 and α = A) B) C) D ) 32) Find the critical X2 -value to test the claim σ2 > 1.9 if n = 18 and α = A) B) C) D ) 33) Compute the standardized test statistic, X2, to test the claim σ2 = 21.5 if n = 12, s2 = 18, and α = A) B) C) D ) A-5

6 Answer Key Testname: UNTITLED1 1) D 2) C 3) D 4) B 5) C 6) B 7) D 8) D 9) A 10) C 11) D 12) A 13) A 14) B 15) B 16) A 17) C 18) C 19) A 20) D 21) B 22) B 23) C 24) D 25) B 26) B 27) C 28) A 29) B 30) C 31) B 32) A 33) D A-6