Chapter 23-25 Multiple Choice Exam Review
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Chapter 25 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Indicate the correct test procedure and reasoning. 1) A teacher is interested in performing a hypothesis test to compare the mean math score of the girls and the mean math score of the boys. She randomly selects 10 girls from the class and then randomly selects 10 boys. She arranges the girls' names alphabetically and uses this list to assign each girl a number between 1 and 10. She does the same thing for the boys. A) Paired t-test. Since there are 10 boys and 10 girls, we can link the two samples. B) Paired t-test. Since the boys and girls are in the same class, and are hence dependent samples, they are can be linked. C) Either two-sample or paired t-test will work. D) Two-sample t-test. There is no natural pairing between the two populations. E) 1-sample t-test. The teacher should compare the sample mean for the girls against the population mean for the boys. 2) A researcher is interested in investigating whether people perform better at dexterity tests while listening to classical music or to no music. He designs a dexterity test, and first gives it to his participants while classical music is playing, and then while no music is playing. A) 1-sample t-test, since there is only one sample of subjects taking the dexterity tests. B) Two-sample t-test, since how a subject performs with music should have no influence on how he performs without music, creating two independent samples. C) Paired t-test, since there are two sets of measurements on the same subjects, providing a natural linking. D) Not enough information is given to determine the best type of test. E) z-test, since the researcher can find the standard deviation of his population.
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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Decide whether or not the conditions and assumptions for inference with a paired t-test are satisfied. Explain your answer. 3) A consumer is interested in investigating the difference in price between regular and 3) premium gasoline at major filling stations. An independent, random sample of stations is chosen and the prices per gallon are recorded for regular and premium gasoline. Regular Premium Station ($/gal) ($/gal) A 1.62 1.75 B 1.52 1.59 C 1.32 2.12 D 2.02 2.14 E 1.98 2.21 F 1.83 1.89 G 1.65 1.91 H 1.91 2.02 I 1.75 1.89
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the paired t-interval procedure to obtain the required confidence interval for the mean difference. Assume that the conditions and assumptions for inference are satisfied. 4) An agricultural company wanted to know if a new insecticide would increase corn yields. Eight 4) test plots showed an average increase of 3.125 bushels per acre. The standard deviation of the increases was 2.911 bushels per acre. Determine a 99% confidence interval for the mean increase in yield. A) (1.851, 6.726) B) (1.851, 4.399) C) (-6.726, -4.399) D) (-0.476, 6.726) E) (-0.476, 4.399)
Interpret the given confidence interval. 5) A high school coach uses a new technique in training middle distance runners. He records the times for 4 different athletes to run 800 meters before and after this training. A 90% confidence interval for the difference of the means before and after the training, µB - µA, was determined to be
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(2.6, 4.8). A) We know that 90% of all random samples done on runners at this high school will show that the mean time difference before and after the training is between 2.6 and 4.8 seconds. B) We are 90% confident that a randomly selected middle distance runner at this high school will have a time for the 800-meter run that is between 2.6 and 4.8 seconds shorter after the training than before the training. C) Based on this sample, with 90% confidence, the average time for the 800-meter run for middle distance runners at this high school is between 2.6 and 4.8 seconds shorter after the new training. D) We know that 90% of the middle distance runners shortened their times between 2.6 and 4.8 seconds after the training. E) Based on this sample, with 90% confidence, the average time for the 800-meter run for middle distance runners at this high school is between 2.6 and 4.8 seconds longer after the new training.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use a paired t-test to perform the required hypothesis test for two population means. Assume that the conditions and assumptions for inference are satisfied. 6) Five students took a math test before and after tutoring. Their scores were as follows. 6) Subject A Before 67 After 71
B C 75 79 84 77
D 69 72
E 75 87
Do the data suggest that the tutoring has an effect on the math scores? Perform a paired t-test at the 5% significance level.
Provide an appropriate response. 7) Ten different families are tested for the number of gallons of water they use each day before and after viewing a conservation video. We want to see if there is strong evidence that the conservation video changes people's water consumption rate. A t-test of the null hypothesis of no difference has a t-statistic of 2.894 with a P-value of 0.0178. Interpret this result by explaining the meaning of the P-value. 2
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8) Ten different families are tested for the number of gallons of water they use each day before and after viewing a conservation video. We want to see if there is strong evidence that the conservation video reduces people's water consumption rate. A t-test of the null hypothesis of no difference has a t-statistic of 2.894 with a P-value of 0.0089. State your conclusion regarding the hypotheses. If this conclusion is incorrect, which type of error was made?
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 9) At one SAT test site students taking the test for a second time volunteered to inhale supplemental oxygen for 10 minutes before the test. In fact, 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-sample t-test C) 1-sample t-test D) matched pairs t-test E) 2-proportion z-test 10) A survey asked people "On what percent of days do you get more than 30 minutes of vigorous exercise?" Using their responses we want to estimate the difference in exercise frequency between men and women. We should use a A) 1-proportion z-interval B) matched pairs t-interval C) 2-proportion z-interva D) 2-sample t-interval E) 1-sample t-interval SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 11) You need to find a new hair stylist and know that there are two terrific salons in your area, Hair by Charles and Curl Up & Dye. You want a really good haircut, but you do not want to pay too much for the cut. A random sample of costs for 10 different stylists was taken at each salon (each salon employs over 100 stylists). Indicate what inference procedure you would use to see if there is a significant difference in the costs for haircuts at each salon. Check the appropriate assumptions and conditions and indicate whether you could or could nor proceed. (Do not do the actual test.)
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12) A packing company considers hiring a national training consultant in hopes of improving productivity on the packing line. The national consultant agrees to work with 18 employees for one week as part of a trial before the packing company makes a decision about the training program. The training program will be implemented if the average product packed increases by more than 10 cases per day per employee. The packing company manager will test a hypothesis using = 0.05. Write appropriate hypotheses (in words and in symbols).
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Answer Key Testname: CH 25 MC FRQ REVIEW 2016
1) D 2) C 3) The data are paired by filling station. The stations are an independent, random sample and represent fewer than 10% of all stations. The boxplot of the differences shows an outlier (0.80) for filling station C.
With the outlier deleted, the boxplot appears fairly symmetric.
With the outlier deleted, the assumptions and conditions for inference are satisfied. 4) D 5) C 6) H : µ =0 0 d H :µ 0 A d Test statistic: t = -2.134 P-value = 0.0998 Do not reject H . At the 5% significance level, the data do not provide sufficient evidence to conclude that the tutoring 0 has an effect on the math scores. 7) If there is no difference in water consumption rates after viewing the conservation video, the chance of seeing a difference as large or larger than the one observed is about 1.78%. 8) The data provide evidence that the conservation video is helpful in reducing people's water consumption. If this conclusion is incorrect, a type I error has been made. 9) E 10) D 11) Use a two-sample t-test for the difference of means. Conditions: * Independent group assumption: Stylists from two different salons are definitely independent groups. * Randomization condition: We are told that these are random samples of stylists from each salon. * 10% condition: The sample represents less than 10% of all possible stylists from each salon. * Nearly Normal condition: We do not have the data, so we do not know about this condition. We would proceed with caution. 12) Ho: µd = 10; The difference between the mean number of cases before and after the training program is not more than 10. HA: µd > 10; The difference between the mean number of cases before and after the training program is more than 10.
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