MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. describes the.

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1 Practice Test 3 Math 1342 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) The term z α/2 σn describes the. 1) A) maximum error of estimate B) unbiased estimator C) confidence interval D) interval estimate 2) Find the critical value z α/2 needed to construct a(n) 79% confidence interval. A) 1.98 B) 0.81 C) 1.25 D) ) A sample of 35 different payroll departments found that employees worked an average of days a year. If the population standard deviation is 18.8 days, find the 90% confidence interval for the average number of days µ worked by all employees who are paid through payroll departments. A) < µ < B) < µ < C) < µ < D) < µ < ) Identify the degree of confidence displayed in the confidence interval shown below. 2) 3) 4) A) 95% B) 99% C) 90% D) 98% 5) In a study using 8 samples, and in which the population variance is unknown, the distribution that should be used to calculate confidence intervals is A) a t distribution with 9 degrees of freedom. B) a standard normal distribution. C) a t distribution with 8 degrees of freedom. D) a t distribution with 7 degrees of freedom. 5) 1

2 Provide an appropriate response. 6) A random sample of 40 college students has a mean earnings of $3120 with a standard deviation of $677 over the summer months. Determine whether a normal distribution or a t-distribution should be used or whether neither of these can be used to construct a confidence interval. A) Cannot use normal distribution or t-distribution. B) Use the t-distribution. C) Use normal distribution. 6) 7) A sample of size n = 21 is drawn from a normal population. Find the critical value t α/2 needed to construct a 90% confidence interval. A) B) C) D) ) A sample of 125 tobacco smokers who recently completed a new smoking-cessation program were asked to rate the effectiveness of the program on a scale of 1 to 10, with 10 corresponding to "completely effective" and 1 corresponding to "completely ineffective". The average rating was 4.1 and the standard deviation was ) 8) Construct a 95% confidence interval for the mean score. A) 0 < µ < 4.1 B) 3.4 < µ < 4.8 C) 3.7 < µ < 4.5 D) 3.8 < µ < 4.4 9) In a survey of 246 registered voters, 132 of them wished to see Mayor Waffleskate lose her next election. Find a point estimate for the proportion of registered voters who wish to see Mayor Waffleskate defeated. A) 132 B) C) D) ) 10) If p^ is equal to 0.88, then q^ is equal to. A) 0.12 B) 0.50 C) 0.45 D) ) The Academy of Orthopedic Surgeons states that 80% of women wear shoes that are too small for their feet. A researcher wants to be 98% confident that this proportion is within 3 percentage points of the true proportion. How large a sample is necessary? A) 484 B) 683 C) 966 D) ) 11) 12) What is the value for χ 2 left for a 95% confidence interval when n = 18? 12) A) B) C) D) ) Find χ 2 left and χ 2 right for a 90% confidence interval using the chi-square distribution 13) with 15 degrees of freedom. A) 7.261, B) 7.790, C) 8.547, D) 6.571,

3 14) Find the 95% confidence interval for the standard deviation of the lengths of pipes if a sample of 11 pipes has a standard deviation of 8.6 inches. A) 63.0 < σ < 85.0 B) 7.6 < σ < 9.6 C) 6.0 < σ < 15.1 D) 36.1 < σ < ) Construct a 99% confidence interval for the population standard deviation σ if a sample of size 11 has standard deviation s = 15. A) 9.62 < σ < B) 9.85 < σ < C) 9.45 < σ < D) 9.17 < σ < ) Determine whether the outcome is a Type I error, a Type II error, or a correct decision. A test is made of H 0 : µ = 40 versus H 1 : µ 40. The true value of µ is 40 and H 0 is rejected. A) Type II error B) Correct decision C) Type I error 17) Determine whether the outcome is a Type I error, a Type II error, or a correct decision. A test is made of H 0 : µ = 16 versus H 1 : µ 16. The true value of µ is 19 and H 0 is not rejected. A) Type I error B) Correct decision C) Type II error 18) Which type of null hypothesis is used in the figure below? 14) 15) 16) 17) 18) A) H 0 : µ k B) H 0 : µ = k C) H 0 : µ k D) H 0 : µ k 19) Which type of alternative hypothesis is used in the figure below? 19) A) H 1 : µ k B) H 1 : µ = k C) H 1 : µ < k D) H 1 : µ > k 3

4 20) Using the z table, find the critical value (or values) for an α = left-tailed test. A) B) C) D) ) 21) A garbage collector believes that he averages picking up more than four tons of garbage per day. What is the null hypothesis for his statement? A) H 0 : µ = 4 B) H 0 : µ 4 C) H 0 : µ 4 D) H 0 : µ < 4 21) 22) A sample of 85 chewable vitamin tablets have a sample mean of 272 milligrams of vitamin C. Nutritionists want to perform a hypothesis test to determine how strong the evidence is that the mean mass of vitamin C per tablet differs from 270 milligrams. State the appropriate null and alternate hypotheses. A) H 0 : µ 270, H 1 : µ = 270 B) H 0 : µ 272, H 1 : µ = 272 C) H 0 : µ = 270, H 1 : µ 270 D) H 0 : µ = 272, H 1 : µ ) 23) A grocery store owner claims that the mean amount spent per checkout is more than $56. A test is made of H 0 : µ = 56 versus H 1 : µ > 56. The null hypothesis is rejected. State the appropriate conclusion. A) There is not enough evidence to conclude that the mean checkout price is greater than $56. B) There is not enough evidence to conclude that the mean checkout price is less than or equal to $56. C) The mean checkout amount is less than or equal to $56. D) The mean checkout amount is greater than $56. 23) 24) A garden supplier claims that its new variety of giant tomato produces fruit with an mean weight of 46 ounces. A test is made of H 0 : µ = 46 versus H 1 : µ 46. The null hypothesis is not rejected. State the appropriate conclusion. A) The mean weight is not equal to 46 ounces. B) There is not enough evidence to conclude that the mean weight is 46 ounces. C) There is not enough evidence to conclude that the mean weight differs from 46 ounces. D) The mean weight is equal to 46 ounces. 24) 25) A test is made of H 0 : µ = 54 versus H 1 : µ 54. A sample of size n = 73 is drawn, and 25) x = 57. The population standard deviation is σ = 21. Compute the value of the test statistic z. A) 0.14 B) 5.59 C) 0.89 D)

5 26) A test is made of H 0 : µ = 50 versus H 1 : µ 50. A sample of size n = 71 is drawn, and 26) x = 56. The population standard deviation is σ = 29. Compute the value of the test statistic z and determine if H 0 is rejected at the α = 0.05 level. A) 0.21, H 0 rejected B) 1.74, H 0 not rejected C) 1.74, H 0 rejected D) 0.21, H 0 not rejected 27) When conducting a two-tailed z test with α = 0.01, the test value was computed to be The decision would be to not reject the null hypothesis. A) True B) False 27) 28) At a certain university, the average cost of books was $370 per student last semester and the population standard deviation was $80. This semester a sample of 45 students revealed an average cost of books of $390 per student. The Dean of Students believes that the costs are greater this semester. What is the test value for this hypothesis? A) 0.44 B) C) 0.25 D) ) 29) What is the critical value for a right-tailed t test when α = and n = 13? A) B) C) D) ) 30) According to Beautiful Bride magazine, the average age of a groom is now 26.2 years. A sample of 16 prospective grooms in Chicago revealed that their average age was 26.6 years with a standard deviation of 5.3 years. What is the test value for a t test of the claim? A) 0.59 B) 1.81 C) 0.30 D) ) 31) The following display from a TI-84 Plus calculator presents the results of a hypothesis test for a population mean µ. 31) µ < 33 t = p = x = Sx = n = 43 What is the value of x? A) B) C) D) 33 5

6 32) In a simple random sample of size 88, there were 22 individuals in the category of interest. It is desired to test H 0 : p = 0.31 versus H 1 : p < Compute the test statistic z. A) 4.97 B) 0.25 C) D) ) 33) In a survey of 702 cigarette smokers, 56 of them reported that they have tried hypnosis therapy to try to quit smoking. Can you conclude that less than one-tenth of smokers have tried hypnosis therapy? Use the α = 0.05 level of significance. A) No conclusion is possible. B) Yes C) No 33) 34) A political strategist claims that 56% of voters in Madison County support his candidate. In a poll of 300 randomly selected voters, 150 of them support the strategist's candidate. At α = 0.05, is the political strategist's claim warranted? A) Yes, because the test value is in the noncritical region. B) No, because the test value is in the critical region. C) Yes, because the test value is in the critical region. D) No, because the test value is in the critical region. 34) 35) A scientist claims that only 65% of geese in his area fly south for the winter. He tags 65 random geese in the summer and finds that 20 of them do not fly south in the winter. If α = 0.05, is the scientist's belief warranted? A) Yes, because the test value 0.72 is in the noncritical region. B) No, because the test value is in the noncritical region. C) Yes, because the test value is in the noncritical region. D) No, because the test value 0.79 is in the critical region. 35) 6