For Problems 20-25, refer to the statement below: Lets admit it. You speed on Hw

Question

For Problems 20-25, refer to the statement below: Lets admit it. You speed on Hwy 34, I speed on Hwy 34, we all speed on Hwy 34. We have people to see, things to do, and that road is boring. A cop was interested in estimating the proportion of people that speed along Hwy 34 and out of those that are speeding, she would like to estimate the average speed people are travelling. Out of the randomly selected 174 people that passed her in an 8-hour time period, only 22 of them were speeding. Out of the 22 that were speeding, their average speed was 72 mph with a sample standard deviation of5 mph. 20. What distribution should you use to compute a confidence interval for the average rate that people speeding travel? a. The t distribution with 21 degrees of freedom. b. The t distribution with 22 degrees of freedom. c. The t distribution with 174 degrees of freedom. d. The t distribution with 173 degrees of freedom e. The z distribution. 21, what is a correct 98% confidence interval for the average rate that people speeding travel? a. 72 +/-2.518 5/sqrt(21) 72 +/-2.747 b. 72 +/-2.518*5/sqrt(22) 72+-2.684 c. 72+/-2.326*5/sqrt(174) 72 +/- 0.882 d. 72 +/-2.326 5/sqrt(173) 72+/-0.884 22. What distribution should you use to compute a confidence interval for the proportion of people that speed along Hwy 34? a. The t distribution with 21 degrees of freedom b. The t distribution with 22 degrees of freedom. c. The t distribution with 174 degrees of freedom. d. The t distribution with 173 degrees of freedom. e. The z distribution 23. Give an approximate 90% confidence interval for the proportion of people that speed along Hwy 34 a. 0.126 +/-1.960 sqrt(0.126*0.874/22) b. 0.126+/- 1.645*sqrt(0.126*0.874/22) c. 0.126 +/-1.960*sqrt(0.126*0.874174) d. 0.126+/- 1.645*sqrt(0.126*0.874/174) 24. Suppose the cop wants to repeat this experiment several months later. How many drivers must she sample in order to produce a 90% confidence interval for the proportion who are speeding along Hwy 34, with a margin of error of two percent? b. 745 d. 2130 e. None of these 25. Suppose the cop wants to repeat this experiment several months later. How many people speeding must she sample in order to produce a 95% confidence interval for the a that people speeding travel, with a margin of error of 0.5 mph? a. 312 verage r ate b. 1501 c. 220 e. None of these

Explanation / Answer

20)
df =n-1 = 22-1 = 21
a) t distribution with 21 degree of freedom

21)
mean = 72 , sd = 5
(mean +- t* sd/sqrt(n))
for 98 % confidence level
t = 2.518
hence
option B) is correct

22)
e) z distribution

23)
p^ = X/n = 22/174 = 0.126
90 % , z = 1.645
se(p^) = sqrt(pq/n)
hence
d) is correct

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