7. A random sample of 862 National Rifle Association (NRA) members gun control l

Question

7. A random sample of 862 National Rifle Association (NRA) members gun control legislation. The survey found that!9.7%of those surveyed supported stricter laws covering the sale of firearms. was surveyed about [2 pts) Is the value 19.7% a parameter or a statistic? Circle one. (A) Parameter (B) Statistic a. b. [4 pts] As suming a long-run proportion of 0.5, a simulated null distribution of 1000 sample proportions gave a mean of 0.501 and a standard deviation of 0.017. Use the 2SD Method to calculate an approximate 95% confidence interval for c. [3 pts] Write a sentence interpreting your interval from part b. in context of the problem (If you were unable to complete part b., state a made-up interval and interpret your made- up interval.) 13 pts] Does this study allow us to generalize our results to the population of all US adults? Explain. d. 8. A tire manufacturer designed a new tread pattern for its all-weather tires. Repeated tests were conducted on cars of approximately the same weight traveling at 60 miles per hour. The tests showed that the new tread pattern enables the cars to stop completely in an average distance of 130 feet with a standard deviation of 7.5 feet and that the stopping distances are approximately normally distributed. [4 pts] Fill in the two blanks below: About 95% of cars of approximately the same weigh traveling at 60 miles per hour will stop completely in a distance of between a. and feet. b. [2 pts] What is the value of the 50h percentile of the distribution of stopping distances?

Explanation / Answer

a. The parameter is drawn from measurement of units in the population. The statistic is drawn from measurement of elements in the sample.

So 19.7% is a statistic. The answer is B.

b. The 95% confidence interval is denoted by a range of 2 standard deviations around mean.

The required interval is (0.501 - 2*0.017, 0.501 + 2x 0.017) i. e., (0.467, 0.535)

c. We can conclude that approximately 95% of the values lie in the confidence interval (0.467,0.535).

d. The result of the survey, the proportion 19.7% or 0.197 lies outside the confidence limit. So we can reject the Null hypothesis.

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