6.19

1. No; we can only say with 95% confidence the true population percent falls in that range.
2. Answers will vary.
3. 0.0051.
4. No; the error assumes a simple random sample with a known population standard deviation.

6.21 n=73.

6.23 No; confidence interval methods of this chapter can only be used on an SRS.

6.25

1. 0.7738.
2. 0.9510.
3. 0.99488, or about 99.5%.

6.27

1. Hypotheses should be stated in terms of the population mean, not the sample mean.
2. The null hypothesis H0 should be that there is no change.
3. A small P-value is needed for significance.
4. We compare the P-value, not the z-statistic, to α.

6.29

1. H0: μ=77 versus Ha: μ≠77.
2. H0: μ=20 seconds versus Ha: μ>20 seconds.
3. H0: μ=880 ft2 versus Ha: μ<880 ft2.

6.31

1. H0: μ=$78,800 versus Ha: μ>$78,800.
2. H0: μ=0.4 versus Ha: μ≠0.4.
3. H0: μ=2 versus Ha: μ<2.

6.33

1. P-value=0.9952.
2. P-value=0.0048.
3. P-value=0.0096.

6.35 H0: μ=$50,994 versus Ha: μ≠$50,994. z=3.76. P-value<0.0001.

6.37 P=0.09 means there is some evidence for the wage decrease, but it is not significant at the α=0.05 level.

6.39 Even if the two groups (the health and safety class and the statistics class) had the same level of alcohol awareness, there might be some difference in our sample due to chance. The difference observed was large enough that it would rarely arise by chance.

6.41 H0: μ=100 versus Ha: μ≠100. z=5.75. P-value<0.0001.

6.43

1. z=1.66. P-value=0.0485.
2. The important assumption is that this is an SRS from the population of older students. We also assume a Normal distribution, but this is not crucial, provided that there are no outliers and there is little skewness.

6.45 H0: μ=26.0 versus Ha: μ<26.0. z=−2.35. P-value=0.0094.

6.47 Smaller α means that x¯ must be farther away from μ0 in order to reject H0.

6.49 With n=100, sample means greater than 0.2 are statistically significant.

6.51 The P-values are doubled.

6.53 Something that occurs “fewer than 1 time in 100 repetitions” must also occur “fewer than 5 times in 100 repetitions,” so significance at the 1% level guarantees significance at the 5% level.

6.55 Any 2.576≤ | z |<2.807.

6.57 P-value=0.1515.

6.59 0.05<P-value < 0.10; P-value=0.0602.

6.61 The first test was barely significant at α=0.05, and the second was significant at any reasonable α.

6.63 A significance test answers only question (b).

6.65

1. If SES had no effect on LSAT results, there would still be some difference in scores due to chance variation.
2. Knowing that the effects were small tells us that the statistically insignificant test result did not occur merely because of a small sample size.

6.67

1. P=0.2843.
2. P=0.1020.
3. P=0.0023.

6.69 We expect more variation with small sample sizes than with large sample sizes, so even a large difference between x¯ and μ0 might not turn out to be significant.

6.71 Answers will vary.

6.73 When you test factors repeatedly, there is a family-wise error rate that needs to be controlled for.

6.75 We would need n=100,000 tests.

6.77 We reject the 5th (P-Value=0.001) and 11th (P-value<0.002) tests.

6.79

1. The manufacturer needs to decide whether the battery is compliant versus noncompliant.
2. Type I error: The manufacturer says the batteries are noncompliant when they are in fact compliant. Type II error: The manufacturer says the batteries are compliant when they are noncompliant.

6.81

1. Type I error: They say there is strong evidence that the student population differs from adults when it does not. Type II error: Conclude that there is not strong evidence that the student population differs from adults when it does.
2. They conclude that there is not strong evidence that the student population mean at your university differs that from the large population of adults; this is a possible Type II error.

6.83

1. Power=0.57.
2. Power=0.81.
3. Power=0.92.

6.85

1. Smaller.

6.87

1. The hypotheses are “subject should go to college” and “subject should join workforce.” Errors: Recommending college for someone better suited for the workforce and recommending the workforce for someone who should go to college.
2. We typically wish to decrease the probability of wrongly rejecting H0.

6.89

1. Changing from the one-sided to the two-sided alternative decreases power.
2. Decreasing σ increases power.
3. Power increases.

6.91 It would be (−∞, ∞), which is useless for identifying μ.

6.93

1. For example, if μ is the mean difference in scores, H0: μ=0 versus Ha: μ≠0.
2. P-value=0.13, we would not reject H0.
3. For example: Was this an experiment? What was the design? How big were the samples?

6.95

1. For boys:

   Energy (kJ)	2399.9 to 2496.1
   Protein (g)	24.00 to 25.00
   Calcium (mg)	315.33 to 332.87

2. For girls:

   Energy (kJ)	2130.7 to 2209.3
   Protein (g)	21.66 to 22.54
   Calcium (mg)	257.70 to 272.30

3. Because the confidence interval for boys is entirely above the confidence interval for girls for each food intake, we could conclude that boys consume more of each, on average.

6.97 Most students should find that their final proportion is between 0.84 and 0.96; 85% will have a proportion between 0.87 and 0.93.

6.99 Because there is nonresponse, the accuracy is in question, regardless of the small margin of error.

6.101

1. Under H0, x¯ has an N(0%, 5.3932%) distribution.
2. z=1.28. P=0.1003.
3. This is not significant at α=0.05.

6.103 Yes.

6.105 For each sample, find x¯ and then take x¯±2.53.

6.107 For each sample, find x¯ and then compute z=x¯−245/15, and reject H0 based on your chosen α.

6.109

1. 4.61 to 6.05 mg/dl.
2. H0: μ=4.8 mg/dl versus Ha: μ>4.8 mg/dl, z=1.45. P-value=0.0735.

6.111

1. The distribution is roughly symmetric.
2. (26.06, 37.74).
3. H0: μ=25. Ha: μ>25, z=2.44. P-value=0.0073.