782 APPENDIX D 19. 0.0000540 (Table: 0.0001). If the mean really is 0 lb as assumed, the probability of getting a sample with a mean of 3.0 lb or higher is very small, so the mean of 3.0 lb is significantly high. There is strong evidence suggesting that the mean is actually higher than 0 lb, so the diet does appear to be effective. However, the mean weight loss of only 3.0 lb is not very much, so even though the diet appears to be effective, it doesn’t appear to be worth using this diet. The amount of weight loss appears to have statistical significance but not practical significance. Section 6-5 1. The requirement is satisfied because the sample size of 147 is greater than 30. 3. Either the points are not reasonably close to a straight-line pattern, or there is some systematic pattern that is not a straight-line pattern. 5. Normal. The points are reasonably close to a straight-line pattern, and there is no other pattern that is not a straight-line pattern. 7. Not normal. The points are not reasonably close to a straight-line pattern, and there appears to be a pattern that is not a straight-line pattern. 9. Normal 11. Not normal 13. Normal 15. Not normal 19. The formula yields P102 = 0.25, P10.52 = 0.5, and P112 = 0.25, which does describe the sampling distribution of the sample proportions. The formula is just a different way of presenting the same information in the table that describes the sampling distribution. Section 6-4 1. The sample must have more than 30 values, or there must be evidence that the population of systolic blood pressures has a normal distribution. 3. m x represents the mean of all sample means, and s x represents the standard deviation of all sample means. For the samples of 36 IQ scores, m x = 100 and s x = 15>236 = 2.5. 5. a. 0.4033 (Table: 0.4052) b. 0.1104 (Table: 0.1112) c. Because the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size. 7. a. 0.2401 (Table: 0.2391) b. 0.6335 (Table: 0.6316) c. Because the original population has a normal distribution, the distribution of sample means is normal for any sample size. 9. a. 0.8534 (Table: 0.8531) b. 0.99999998 (Table: 0.9999) c. It appears that the elevator would be overloaded with 27 adult males, which is probably unlikely but possible. Also, it is likely that a safety factor is built in so that the elevator can safely take a load greater than the 4000 lb capacity on the placard. But to be safe, instead of boarding the elevator full of adult men, it would be wiser to wait for another elevator. 11. a. 140 lb b. 0.9999999998 (Table: 0.9999) c. 0.9458 (Table: 0.9463) d. The new capacity of 20 passengers does not appear to be safe enough because the probability of overloading is too high. 13. a. 0.5575 (Table: 0.5564) b. 0.9996 (Table: 0.9995) c. Part (a) because the ejection seats will be occupied by individual women, not groups of women. 15. a. 0.8877 (Table: 0.8869) b. 1.0000 when rounded to four decimal places (Table: 0.9999) c. The probability from part (a) is more relevant because it shows that 89% of male passengers will not need to bend. The result from part (b) gives us information about the mean for a group of 100 men, but it doesn’t give us useful information about the comfort and safety of individual male passengers. d. Because men are generally taller than women, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women. 17. If we assume that the true mean weight gain is 15 lb, the probability of getting a sample of 67 college students having a mean weight gain of 2.6 lb or less is 0+ (Table: 0.0001). Because it is so unlikely to get a sample such as the one obtained, it appears that the assumption of a mean weight gain of 15 lb is an incorrect assumption. The “Freshman 15” claim of a mean weight gain of 15 lb appears to be an incorrect claim.
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