Exam 4 review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) Which of the following is not a characteristic of Students' t distribution? A) depends on degrees of freedom. B) symmetric distribution C) For large samples, the t and z distributions are nearly equivalent. D) mean of 1 1) 2) Suppose a 95% confidence interval for µ turns out to be (100, 230). To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced interval width? A) All of these. B) Increase the sample size. C) Increase the sample size and decrease the confidence level. D) Decrease the confidence level. 2) 3) If the level of significance is 0.05, and the P-value is 0.043, the decision would be to A) make no decision because the difference between the level of significance and the P-value is not statistically significant. B) use a nonparametric test because normality of the data cannot be established when the results are close. C) fail to reject H0. D) reject H0. 3) 4) Two samples are said to be dependent if A) sampling for inclusion in the two samples is done with replacement. B) the individuals in one sample have no influence over the selection of the individuals in a second sample. C) the individuals in one sample are used to determine the individuals in a second sample. D) some individuals, but not all, in one sample exert influence over who is selected for inclusion in a second ample. 4) 5) Robustness in hypothesis testing means A) all processes can be exactly duplicated by selecting another pair of samples. B) departures from normality do not adversely affect the results. C) the data is effected by outliers. D) there are no departures from normality. 5) 6) When performing a hypothesis test upon two dependent samples, the variable of interest is A) all of the combined data. B) the absolute value of the differences that exist between the matched-pair data. C) the data that is the same in both samples. D) the differences that exist between the matched-pair data. 6) 1
7) A survey of 1010 college seniors working towards an undergraduate degree was conducted. Each student was asked, "Are you planning or not planning to pursue a graduate degree?" Of the 1010 surveyed, 658 stated that they were planning to pursue a graduate degree. Construct and interpret a 98% confidence interval for the proportion of college seniors who are planning to pursue a graduate degree. A) (0.612, 0.690); we are 98% confident that the proportion of college seniors who are planning to pursue a graduate degree is between 0.612 and 0.690. B) (0.620, 0.682); we are 98% confident that the proportion of college seniors who are planning to pursue a graduate degree is between 0.620 and 0.682. C) (0.616, 0.686); we are 98% confident that the proportion of college seniors who are planning to pursue a graduate degree is between 0.616 and 0.686. D) (0.621, 0.680); we are 98% confident that the proportion of college seniors who are planning to pursue a graduate degree is between 0.621 and 0.680. 7) 8) An article a Florida newspaper reported on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the family's financial situation, 37% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national sampling of 531 teenagers. Estimate the proportion of all teenagers who want more family discussions about school. Use a 99% confidence level. A) 0.37 ± 0.054 B) 0.37 ± 0.002 C) 0.63 ± 0.002 D) 0.63 ± 0.054 8) 9) Compute the critical value zα/2 that corresponds to a 94% level of confidence. A) 1.88 B) 2.33 C) 1.645 D) 1.96 9) 10) How much money does the average professional hockey fan spend on food at a single hockey game? That question was posed to 10 randomly selected hockey fans. The sampled results show that sample mean and standard deviation were $15.00 and $2.95, respectively. Use this information to create a 99% confidence interval for the mean. A) 15 ± 3.106(2.95/ 10) B) 15 ± 2.821(2.95/ 10) C) 15 ± 3.25(2.95/ 10) D) 15 ± 3.169(2.95/ 10) 10) 11) A researcher at a major clinic wishes to estimate the proportion of the adult population of the United States that has sleep deprivation. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 5%? A) 271 B) 769 C) 385 D) 10 11) 12) In a recent study of 42 eighth graders, the mean number of hours per week that they played video games was 19.6 with a population standard deviation of 5.8 hours. Compute the 98% confidence interval for µ. A) (14.1, 23.2) B) (18.3, 20.9) C) (17.5, 21.7) D) (19.1, 20.4) 12) 2
13) To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on this cigarette gave a mean nicotine content of 26.6 milligrams and standard deviation of 2.4 milligrams for a sample of n = 9 cigarettes. The FDA claims that the mean nicotine content exceeds 30.3 milligrams for this brand of cigarette, and their stated reliability is 99%. Do you agree? A) Yes, since the value 30.3 does not fall in the 99% confidence interval. B) No, since the value 30.3 does not fall in the 99% confidence interval. C) No, since the value 30.3 does fall in the 99% confidence interval. D) Yes, since the value 30.3 does fall in the 99% confidence interval. 13) 14) A survey claims that 9 out of 10 doctors (i.e., 90%) recommend brand Z for their patients who have children. To test this claim against the alternative that the actual proportion of doctors who recommend brand Z is less than 90%, a random sample of doctors was taken. Suppose the test statistic is z = -2.23. Can we conclude that H0 should be rejected at the a) α =0.10, b) α = 0.05, and c) α = 0.01 level? A) a) no; b) no; c) no B) a) no; b) no; c) yes C) a) yes; b) yes; c) yes D) a) yes; b) yes; c) no 14) 15) The hypothesis contains the "=" sign. A) alternative B) explanatory C) conditional D) null 15) 16) True or False: Results that are statistically significant are always practically significant. A) False B) True 16) 17) The mean age of principals in a local school district is 47.1 years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis? A) There is not sufficient evidence to reject the claim µ = 47.1. B) There is sufficient evidence to support the claim µ = 47.1. C) There is sufficient evidence to reject the claim µ = 47.1. D) There is not sufficient evidence to support the claim µ = 47.1. 17) 18) Given H0: µ 85, H1: µ > 85, and P = 0.005. Do you reject or fail to reject H0 at the 0.01 level of significance? A) reject H0 B) not sufficient information to decide C) fail to reject H0 18) 19) Find the standardized test statistic t for a sample with n = 20, x = 5.6, s = 2.0, and α = 0.05 if H1: µ < 6. Round your answer to three decimal places. A) -0.894 B) -0.872 C) -1.233 D) -1.265 19) 3
20) Find the standardized test statistic to test the hypothesis that µ1 = µ2. Two samples are randomly selected from each population. The sample statistics are given below. Use α = 0.05. n1 = 40 n2 = 35 20) x1 = 13 x2 = 14 s1 = 2.5 s2 = 2.8 A) -2.6 B) -0.8 C) -1.6 D) -1.0 21) In a recent survey of drinking laws, a random sample of 1000 women showed that 65% were in favor of increasing the legal drinking age. In a random sample of 1000 men, 60% favored increasing the legal drinking age. Construct a 95% confidence interval for p1 - p2. A) (-1.423, 1.432) B) (0.008, 0.092) C) (-2.153, 1.679) D) (0.587, 0.912) 21) 22) Classify the two given samples as independent or dependent. Sample 1: Pre-training blood pressure of 19 people Sample 2: Post-training blood pressure of 19 people A) dependent B) independent 22) 23) If the individuals selected for a sample have no influence upon which individuals are selected for a second sample, then the samples are said to be A) independent B) consistent C) inconsistent D) dependent 23) 24) A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.7%, 5%). What is the point estimator of the mean percentage of reservations that are canceled on the day of the flight? A) 3.35% B) 3.3% C) 2.50% D) 1.65% 24) 25) Construct a 90% confidence interval for the population mean, µ. Assume the population has a normal distribution. In a recent study of 22 eighth graders, the mean number of hours per week that they played video games was 19.6 with a standard deviation of 5.8 hours. A) (19.62, 23.12) B) (17.47, 21.73) C) (5.87, 7.98) D) (18.63, 20.89) 25) 26) Many people think that a national lobby's successful fight against gun control legislation is reflecting the will of a minority of Americans. A random sample of 4000 citizens yielded 2200 who are in favor of gun control legislation. Find the point estimate for estimating the proportion of all Americans who are in favor of gun control legislation. A) 2200 B) 4000 C) 0.4500 D) 0.5500 26) 27) Find the standardized test statistic t for a sample with n = 12, x = 18.7, s = 2.1, and α = 0.01 if H1: µ 19.2. Round your answer to three decimal places. A) -0.037 B) -0.008 C) -0.381 D) -0.825 27) 28) Construct a 95% confidence interval for data sets A and B. Data sets A and B are dependent. A 30 28 47 43 31 B 28 24 25 35 22 Assume that the paired data came from a population that is normally distributed. A) (-1.324, 8.981) B) (-0.696, 18.700) C) (-0.113, 12.761) D) (-15.341, 15.431) 28) 4
29) Construct a 95% confidence interval for the population mean, µ. Assume the population has a normal distribution. A random sample of 16 lithium batteries has a mean life of 645 hours with a standard deviation of 31 hours. A) (876.2, 981.5) B) (321.7, 365.8) C) (628.5, 661.5) D) (531.2, 612.9) 29) 30) Suppose you are using α = 0.01 to test the claim that µ 20 using a P-value. You are given the sample statistics n = 40, x = 21.8, and σ = 4.3. Find the P-value. A) 0.0040 B) 0.0211 C) 0.9960 D) 0.1030 30) 31) Construct a 95% confidence interval for µ1 - µ2. Two samples are randomly selected from normal populations. The sample statistics are given below. n1 = 8 n2 = 7 31) x1 = 4.1 x2 = 5.5 s1 = 0.76 s2 = 2.51 A) (2.112, 2.113) B) (-1.132, 1.543) C) (-3.813, 1.013) D) (-1.679, 1.987) 32) A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. Use a 95% confidence interval to estimate the true proportion of students on financial aid. A) 0.59 ± 0.002 B) 0.59 ± 0.005 C) 0.59 ± 0. 474 D) 0.59 ± 0.068 32) 33) True or False: As the level of confidence increases the margin of error decreases. A) True B) False 33) 34) A hypothesis test is a "two-tailed" if the alternative hypothesis contains a sign. A) > B) C) + D) < 34) 35) A local tennis pro-shop strings tennis rackets at the tension (pounds per square inch) requested by the customer. Recently a customer made a claim that the pro-shop consistently strings rackets at lower tensions, on average, than requested. To support this claim, the customer asked the pro shop to string 11 new rackets at 51 psi. Upon receiving the rackets, the customer measured the tension of each and calculated the following summary statistics: x = 47 psi, s = 3.1 psi. In order to conduct the test, the customer selected a significance level of α =.01. Interpret this value. A) The probability of concluding that the true mean is less than 51 psi when in fact it is equal to 51 psi is only.01. B) There is a 1% chance that the sample will be biased. C) The smallest value of α that you can use and still reject H0 is 0.01. D) The probability of making a Type II error is 0.99. 35) 36) If we reject the null hypothesis when the null hypothesis is true, then we have made a A) Correct decision B) Type α error C) Type II error D) Type I error 36) 37) If we do not reject the null hypothesis when the null hypothesis is in error, then we have made a A) Type β error B) Type II error C) Correct decision D) Type I error 37) 5
38) The level of significance, α, is the probability of making a A) Type I error B) Correct decision C) Type II error D) Type β error 38) 39) Find the standardized test statistic, z, to test the hypothesis that p1 < p2. Use α = 0.10. The sample statistics listed below are from independent samples. Sample statistics: n1 = 550, x1 = 121, and n2 = 690, x2 = 195 A) -2.132 B) 1.116 C) -0.985 D) -2.513 39) 40) What is the H0 for testing differences of the means of two independent samples? A) H0:µ1 > µ2 B) H0:µ1 < µ2 C) H0:µ1 - µ2 = 0 D) H0:µ1 µ2 40) Construct a 95% Z-interval or a 95% t-interval about the population mean. Assume the data come from a population that is approximately normal with no outliers. 41) The heights of 20- to 29-year-old females are known to have a population standard deviation 41) σ = 2.7 inches. A simple random sample of n = 15 females 20 to 29 years old results in the following data: 63.1 67.9 64.8 62.2 65.4 63.3 66.2 68.2 69.7 64.1 68.4 69.9 67.3 64.5 70.2 A) (64.85, 67.85); we are 95% confident that the mean height of 20- to 29-year-old females is between 64.85 and 67.85 inches. B) (64.98, 67.72); we are 95% confident that the mean height of 20- to 29-year-old females is between 64.98 and 67.72 inches. C) (65.20, 67.50); we are 95% confident that the mean height of 20- to 29-year-old females is between 65.20 and 67.50 inches. D) (65.12, 67.58); we are 95% confident that the mean height of 20- to 29-year-old females is between 65.12 and 67.58 inches. 6