Section 9.3 Hypothesis Tests for a Population Mean, Standard Deviation Unknown 445 11.90 11.95 12.00 12.05 12.10 12.15 b. If appropriate, perform a hypothesis test to determine whether the mean volume differs from 12 ounces. Use the �� = 0.05 level of significance. What do you conclude? Do not reject H0. 23. Credit card debt: Following are outstanding credit card balances for a sample of 16 college seniors at a large university. 870 419 1021 723 152 387 335 334 2618 529 593 769 502 485 1213 347 a. Following is a dotplot for these data. Is it reasonable to assume that the conditions for performing a hypothesis test are satisfied? Explain. No 0 500 1000 1500 2000 2500 3000 b. According to the report How America Pays for College, by Sallie Mae, the mean outstanding balance for college seniors in 2012 was $515. If appropriate, perform a hypotheis test to determine whether the mean debt for seniors at this university differs from $515. Not appropriate 24. Rats: A psychologist is designing an experiment in which rats will navigate a maze. Ten rats run the maze, and the time it takes for each to complete the maze is recorded. The results are as follows. 66.3 68.1 52.5 68.3 62.6 55.6 42.1 60.9 69.2 69.3 a. Following is a boxplot for these data. Is it reasonable to assume that the conditions for performing a hypothesis test are satisfied? Explain. No 40 45 50 55 60 65 70 b. The psychologist hopes that the mean time for a rat to run the maze will be greater than 60 seconds. If appropriate, perform a hypotheis test to determine whether the mean time is greater than 60 seconds. Not appropriate 25. Keep cool: Following are prices, in dollars, of a random sample of ten 7.5-cubic-foot refrigerators. 314 377 330 285 319 274 332 350 299 306 a. Following is a dotplot for these data. Is it reasonable to assume that the conditions for performing a hypothesis test are satisfied? Explain. Yes 260 280 300 320 340 360 380 b. A consumer organization reports that the mean price of 7.5-cubic-foot refrigerators is greater than $300. Do the data provide convincing evidence of this claim? Use the �� = 0.01 level of significance. Do not reject H0. 26. Free dessert: In an attempt to increase business on Monday nights, a restaurant offers a free dessert with every dinner order. Before the offer, the mean number of dinner customers on Monday was 150. Following are the numbers of diners on a random sample of 12 days while the offer was in effect. 206 169 191 152 212 139 142 151 174 220 192 153 a. Following is a boxplot for these data. Is it reasonable to assume that the conditions for performing a hypothesis test are satisfied? Explain. Yes 120 140 160 180 200 220 240 b. Can you conclude that the mean number of diners increased while the free dessert offer was in effect? Use the �� = 0.01 level of significance. Reject H0. 27. Effective drugs: When testing a new drug, scientists measure the amount of the active ingredient that is absorbed by the body. In a study done at the Colorado School of Mines, a new antifungal medication that was designed to be applied to the skin was tested. The medication was applied to the skin of eight adult subjects. One hour later, the amount of active ingredient that had been absorbed into the skin was measured for each subject. The results, in micrograms, were 1.28 1.81 2.71 3.13 1.55 2.55 3.36 3.86 a. Construct a boxplot for these data. Is it appropriate to perform a hypothesis test? Yes b. If appropriate, perform a hypothesis test to determine whether the mean amount absorbed is greater than 2 micrograms. Use the �� = 0.05 level of significance. What do you conclude? Do not reject H0. 28. More effective drugs: An antifungal medication was applied to the skin of eight adult subjects. One hour later, the amount of active ingredient that had been absorbed into the skin was measured for each subject. The results, in micrograms, were 2.13 1.88 2.07 1.19 2.51 5.61 2.81 3.05 a. Construct a boxplot for these data. Is it appropriate to perform a hypothesis test? No b. If appropriate, perform a hypothesis test to determine whether the mean amount absorbed is less than 3 micrograms. Use the �� = 0.05 level of significance. What do you conclude? Not appropriate 29. Interpret calculator display: The following display from a TI-84 Plus calculator presents the results of a hypothesis test for a population mean ��. a. State the null and alternate hypotheses. H0 : �� = 2, H1: �� < 2 b. What is the value of ̄x? 1.88 c. What is the value of s? 0.21 d. How many degrees of freedom are there? 17 e. Do you reject H0 at the 0.05 level? Explain. Yes f. Someone wants to test the hypothesis H0 : �� = 1.8 versus H1: �� > 1.8. Use the information in the display to compute the t statistic for this test. 1.616 g. Compute the P-value for this test. 0.0622
navidi_monk_elementary_statistics_2e_ch7-9
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