17 One of the different statistics reported by the Centers for Disease Control r
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17 One of the different statistics reported by the Centers for Disease Control regarding incidence of obesity among adults in the United States provides that 27.9% of men with college degree are obese. The study also reports that 31.4% of men without a college degree are obese. Assume the latter statistic is based on a sample of 980 men without a college degree. Does the data provide statistically significant evidence that the incidence of obesity among men without a college degree is greater than among those with a college degree? Compute the p-value for this hypothesis test. p-value = ______. a 0.0344 The evidence is not statistically significant. Reject H. b 0.0344 The evidence is statistically significant. Reject H. c 0.0071 The evidence is statistically significant. Reject H. d 0.0071 The evidence is not statistically significant. Reject H. 18 We want to test the hypothesis that at least 85% of drivers on a freeway violate the speed limit. In a random sample of n = 1,050 vehicles, 83% violated the speed limit. Compute the test statistic. State the null and alternative hypotheses and the decision rule. Use = 0.05. a TS = 1.82 Do not reject H. The proportion of violators is not less than 0.85. b TS = 1.82 Reject H. The proportion of violators is less than 0.85. c TS = 1.45 Do not reject H. The proportion of violators is not less than 0.85. d TS = 1.45 Reject H. The proportion of violators is less than 0.85. 17 One of the different statistics reported by the Centers for Disease Control regarding incidence of obesity among adults in the United States provides that 27.9% of men with college degree are obese. The study also reports that 31.4% of men without a college degree are obese. Assume the latter statistic is based on a sample of 980 men without a college degree. Does the data provide statistically significant evidence that the incidence of obesity among men without a college degree is greater than among those with a college degree? Compute the p-value for this hypothesis test. p-value = ______. a 0.0344 The evidence is not statistically significant. Reject H. b 0.0344 The evidence is statistically significant. Reject H. c 0.0071 The evidence is statistically significant. Reject H. d 0.0071 The evidence is not statistically significant. Reject H. 18 We want to test the hypothesis that at least 85% of drivers on a freeway violate the speed limit. In a random sample of n = 1,050 vehicles, 83% violated the speed limit. Compute the test statistic. State the null and alternative hypotheses and the decision rule. Use = 0.05. a TS = 1.82 Do not reject H. The proportion of violators is not less than 0.85. b TS = 1.82 Reject H. The proportion of violators is less than 0.85. c TS = 1.45 Do not reject H. The proportion of violators is not less than 0.85. d TS = 1.45 Reject H. The proportion of violators is less than 0.85.Explanation / Answer
18) In this example we have given that
n=1050
p^ = sample proportion = 83% = 0.83
Here we have to test the hypothesis that,
H0 : p = 85% = 0.85 Vs H1 : p >=0.85
where p is population proportion.
The test statistic formula is,
Z = (p^ - p) / sqrt [(pq) / n ]
where q = 1 - p
q = 1 - 0.85 = 0.15
Z = (0.83 - 0.85) / sqrt [ (0.85*0.15) / 1050 ]
Z = -0.02 / 0.011 = -1.81
| Z | = | -1.81 |
Z = 1.81
Now we have to find P-value for taking decision.
P-value syntax in EXCEL is,
=NORMSDIST(z)
where z is test statistic value = -1.81
P-value = 0.03
Assume alpha = 0.05
P-value < alpha
Reject H0 at 5% level of significance.
Conclusion : At least 85% of drivers on a freeway violate the speed limit.
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