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Question: In a poll of 600 voters in a campaign to eliminate non-returnable beverage containers, 210 of the voters were opposed. Develop a 92% confidence interval estimate for the proportion of all the voters who opposed the container control bill.
Answer:
92% of confidence interval (CI) for p is given by p±Z0.08 √(pq/n)
Here,
p= 210/600= 0.35 q= (1-p) = 0.65
Z0.08 = 1.75609 n= 600
Hence, CI is
0.35±1.75609 √((0.35*0.65)/600)
= 0.35±0.03409
(0.31591,0.38409)

Question: A random sample of 87 airline pilots had an average yearly income of $99,400 with a standard deviation of $12,000.

1. If we want to determine a 95% confidence interval for the average yearly income, what is the value of t?

Answer: T86(0.05)= 1.987934 2. Develop a 95% confidence interval for the average yearly income of all pilots. Answer: 95% of CI for µ is given by x̅± t0.05 * S/√(n-1) x̅ = ± $99400 n= 87 s= $12000 t0.05= 1.987934
Hence, CI is
= 99400±1.987934 * 12000/(√86)
= ($96827.62677, $101972.37323)
Question 3: In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 25 pieces of carry-on luggage was collected and weighed. The average weight was 18 pounds. Assume that we know the standard deviation of the population to be 7.5 pounds. 3. Determine a 97% confidence interval estimate for the mean weight of the carry-on luggage.
Answer: 97% CI for mean weight is given by x̅ ± Z.03σ/√n
=18± 2.17009(7.5/√25)
= 18 ± 3.255135
=(14.744865 pounds, 21.255135pounds) 4. Determine a 95% confidence interval estimate for the mean weight of the carry-on luggage
95% CI for mean weight is x̅ ± Z.05σ/√n
= 18 ± 1.96 (7.5/√25)
= 18 ± 2.94
= (15.06 pounds, 20.94 pounds)
Question 4: A statistician employed by a consumer testing organization reports that at 95% confidence he has determined that the true average content

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