MATHS 125 QUESTIONS AND ANSWERS EXAMS ELABORATION

MATHS 125 QUESTIONS AND ANSWERS EXAMS ELABORATION Statistics Exam 4 1. In conducting a hypothesis test, which of these are what we are looking for evidence of? 1) B a) the Null Hypothesis (H0) is true b) the Alternative Hypothesis (HA) is true c) the Significance Level (α) d) the Critical Value 2 In a hypothesis test with a significance level, α = 0.05, which of the following P-values would 2) C cause us to reject the Null Hypothesis? a) 1.693 b) 0.55 c) 0.02 d) 0.07 3. When testing a hypothesis regarding the proportion of college students who purchase their 3) A textbooks online, which model would you use? a) Normal b) Student-t c) neither d) It doesn’t matter 4. If a researcher believed that the average young adult (under age 30) carries less than 4) A $10 in cash with them, then the Null Hypothesis for the hypothesis test should be: a) The mean is less than $10 b) The mean is not equal to $10 c) The mean is equal $10 d) The mean is at most $10 5. For a hypothesis test, a sample is gathered. The sample mean and P-value are found. 5) A What is the meaning of the P-value? I) The evidence that supports the alternate. II) The probability of a type I error. III) The probability of getting the sample that we found, given that HO is true. a) III b) I and II c) II d) I and III 6. It is believed that 62% of Americans think that foreign made cars are higher quality 6) D than American made cars. After a recent advertising campaign sponsored by American auto makers, a research company wants to determine if that percentage has decreased. Which inference technique would we use? a) A hypothesis test for means. b) A confidence interval for proportions. c) A confidence interval for means. d) A hypothesis test for proportions. 7. Construct a 95% confidence interval for the difference between the two independent 7) A population means. Brand X BrandY n = 35 n= 40 = 19.4 = 15.1 s = 1.4 s = 0.8 a) (3.8, 4.8) b) (3.6, 5.0) c) (3.5, 5.1) d) (-4.7, -3.9) 8. In order to test whether raw garlic is effective in lowering LDL cholesterol, a group of 49 8) A subjects were treated and the change in their cholesterol levels before and after treatment were analyzed. A hypothesis test was performed with, HO: µd = 0 Raw garlic is not effective in lowering mean LDL cholesterol level. HA: µd < 0 Raw garlic is effective in lowering mean LDL cholesterol level. What conclusion would be made if the P-value was very low? a) There is no evidence that raw garlic is effective in lowering mean LDL cholesterol level. b) There is evidence that raw garlic is not effective in lowering mean LDL cholesterol level. c) There is evidence that raw garlic is effective in lowering mean LDL cholesterol level. d) No conclusion can be made because the sample was too small. 9. The mean weight of a random sample, size 32, of a bag of 500 M&M’s is found. Which of 9) B the conditions to use a student t model to represent the data is not met? a) it is a random sample b) n < 0.05N c) n ≥ 30 or from a Normal population d) all of these conditions are met 10. A survey of several randomly selected hospitals found that 37 of 223 births in Vermont 10) A involved cesarean deliveries, compared to 35 of 186 births in New Hampshire. Is this evidence that the rate of cesarean births in the two states is different? Use α = 0.05. a) P-value = 0.556 0.556 > 0.05 There is no evidence that the rate of cesarean births is different. b) P-value = 0.556 0.556 > 0.05 There is evidence that the rate of cesarean births is different. c) P-value = 0.278 0.278 > 0.05 There is no evidence that the rate of cesarean births is different. d) P-value = 0.278 0.278 > 0.05 There is evidence that the rate of cesarean births is different. 11. We are about to test a hypothesis using data from a well-designed study. Which is true? 11) D a) A large P-value would be strong evidence the null hypothesis is false. b) A large P-value would be strong evidence the null hypothesis is true. c) A small P-value would be strong evidence the alternate hypothesis is false. d) A small P-value would be strong evidence the alternate hypothesis is true. 12. A teacher is interested in performing a hypothesis test to compare the difference between the 12) B mean math score of the girls and the mean math score of the boys. Indicate the correct test procedure and reasoning. a) Paired t-test. Since the boys and girls are in the same class, and are hence dependent samples, they are can be linked. b) Two-sample t-test. There is no natural pairing between the two populations. c) Either two-sample or paired t-test will work. d) Paired t-test. Since there are 10 boys and 10 girls, we can link the two samples. 13. An online catalog company wants on-time delivery for at least 90% of the orders they ship. 13) A They have been shipping orders via UPS and FedEx but will switch to a more expensive service if there is evidence that this service can exceed the 90% on-time goal. The company sends a random sample of orders via ShipFast, and then makes follow-up phone calls to see if these orders arrived on time. Which hypotheses should they test? a) HO: p = 0.90 b) HO: p < 0.90 c) HO: p > 0.90 d) HO: p = 0.90 HA: p > 0.90 HA: p = 0.90 HA: p = 0.90 HA: p < 0.90 14. Absorption rates into the body are important considerations when manufacturing a generic 14) A version of a brand-name drug. A pharmacist read that the absorption rate into the body of a new generic drug (G) is the same as its brand-name counterpart (B). She has a researcher friend of hers run a small experiment to test HO: μG - μB = 0 against the alternative Ha: μG - μB ≠ 0. Which of the following would be a Type I error? a) Deciding that the absorption rates are different, when in fact they are not. b) Deciding that the absorption rates are different, when in fact they are. c) Deciding that the absorption rates are the same, when in fact they are not. d) The researcher cannot make a Type I error, since he ran then experiment. 15. At one SAT test site students taking the test for a second time volunteered to inhale 15) B supplemental oxygen for 10 minutes before the test. Some received oxygen, but others (randomly assigned) were given just normal air. Test results showed that 42 of 66 students who breathed oxygen improved their SAT scores, compared to only 35 of 63 students who did not get the oxygen. Which procedure should we use to see if there is evidence that breathing extra oxygen can help test-takers think more clearly? a) 1-proportion z-test b) 2-proportion z-test c) 1-sample t-test d) 2-sample t-test e) matched pairs t-test 16. A random sample of 120 classrooms at a large university found that 70% of them had been 16) B cleaned properly. What is the standard error of the sample proportion? a) 0.028 b) 0.042 c) 0.046 d) 0.082 17. Researchers wonder if the mean body temperature of humans is greater than 98.6 degrees. 17) D A random sample of n = 18 has a mean of 98.8, a standard deviation of 0.6 degrees and yields a P-value of 0.09. Ho: μ = 98.6, HA: μ > 98.6 At α = 0.05, what would be the conclusion of the researchers? a) Fail to reject the null hypothesis and conclude that the mean temperature is 98.6 b) Fail to reject the null hypothesis and conclude that the mean temperature is greater than 98.6 c) Reject the null hypothesis and conclude that the mean temperature is greater than 98.6 d) Fail to reject the null hypothesis and conclude that there is no evidence that mean temperature is greater than 98.6 18. A high school coach uses a new technique in training middle distance runners. He records 18) B the times for 4 different athletes to run 800 meters before and after this training. A 95% confidence interval for the difference of the means before and after the training was determined to be (2.1, 4.4). Interpret the given confidence interval. a) Based on this sample, with 95% confidence, the average time for the 800-meter run for all middle distance runners at this high school is between 2.1 and 4.4 seconds shorter after the new training. b) We are 95% confident that a randomly selected middle distance runner at this high school will have a time for the 800-meter run that is between 2.1 and 4.4 seconds shorter after the training than before the training. c) We know that 95% of all runners at this high school will show that the mean time difference before and after the training is between 2.1 and 4.4 seconds. d) Based on this sample, with 95% confidence, the time for the 800-meter run for any middle distance runners at this high school is between 2.1 and 4.4 seconds longer after the new training. 19. A company that sells bags of fertilizer installed new filling machines. They wanted to perform a test to see if the mean amount in these bags had changed. Their null hypothesis was that the mean had not changed. The alternate hypothesis was that the mean weight had changed. They took a random sample of 50 bags and found the mean and standard deviation of the sample. They calculated that these results had a P-value of approximately 0.02. This P-value caused them to reject HO at α = 0.05. i) In context, what does this conclusion say? i) A a) The evidence suggests that these bags are being filled with a mean amount that is different. b) We don't have enough evidence to say that these bags are being filled with a mean amount that is different. c) The evidence suggests that these bags are being filled with the same mean amount. ii) How would the conclusion have changed if they had instead used a significance level ii) C of α = 0.01? a) Rejected HA. b) Accept HO c) Failed to reject HO d) They would have reached the same conclusion using either α = 0.05 or α = 0.01 20. Seth is starting his own food truck business, and he's choosing cities where he'll run his 20) C business. He wants to survey residents and test whether or not the demand is high enough to support his business before he applies for the necessary permits to operate in a given city. He'll only choose a city if there's strong evidence that the demand there is high enough. We can state the hypotheses for his test as H0: The demand is not high enough vs. HA: The demand is high enough. What would be the consequence of a Type I error in this setting? a) He doesn't choose a city where demand is actually high enough. b) He chooses a city where demand is actually high enough. c) He chooses a city where demand isn't actually high enough. d) He doesn't choose a city where the demand is not high enough. 21. A restaurant owner installed a new automated drink machine. The machine is designed to 21) C dispense 530 ml of liquid on the medium size setting. The owner suspects that the machine may be dispensing too much in medium drinks. They decide to take a sample of 30 medium drinks to see if the mean amount is significantly greater than 530 ml. What are appropriate hypotheses for their significance test? a) HO: p = 530, HA: p > 530 b) HO: p = 530, HA: p < 530 c) HO: μ = 530, HA: μ > 530 d) HO: μ = 530, HA: μ < 530 22. Donated blood is tested for infectious diseases and other contaminants. Since most donated 22) D blood is safe, workers save time and money by testing batches of donated blood rather than testing individual samples. Workers perform a test to check if a certain toxin is present, and the entire batch is discarded if the toxin is detected. This is similar to using a null and an alternative hypothesis to determine whether to discard the batch. The hypotheses being tested could be stated as: H0: The batch does not contain the toxin. Ha: The batch contains the toxin. Under which of the following conditions would the testers commit a Type II error? a) The batch does not actually contain the toxin, and they conclude it does not. b) The batch does not actually contain the toxin, and they conclude it does. c) The batch actually contains the toxin, and they conclude it does. d) The batch actually contains the toxin, and they conclude it does not. 23. A sociologist was curious about how much smartphone access has changed for American 23) A teenagers. They obtained separate random samples of teenagers from 2017 and 2013. Here are their results: Has access to smartphone? 2017 2013 Yes 450 120 No 150 280 Total 600 400 They want to use these results to construct a 95% confidence interval to estimate the difference in the proportion of teens each year who had access to a smartphone (p2017 − p2013). Which of the following is a correct 95% confidence interval based on their data? a) (0.393, 0.507) b) (0.023, 0.168) c) (0.127, 0.449) d) (0.410, 0.523) 24. Researchers want to study the effectiveness of a new medication to treat depression. In a 24) C randomized experiment, 71 out of 200 people taking the medication report symptoms of depression. Of the people receiving a placebo, 92 out of 200 report symptoms of depression. The researchers want to use these results to test if the medication is working any differently than the placebo. Let p1 be the true proportion of individuals like the ones in this study who take the new medication and report symptoms of depression, and p2 be the true proportion of individuals like the ones in this study who take a placebo and report symptoms of depression. Which of the following is an appropriate set of hypotheses for their significance test? a) H0: p1 = p2 b) H0: p1 = p2 c) H0: p1 = p2 d) H0: p1 ≠ p2 Ha: p1 < p2 HA : p1 > p2 HA: p1 ≠ p2 HA : p1 = p2