1. A random sample of 4,000 U.S. citizens was asked their opinion concerning gun
ID: 3318709 • Letter: 1
Question
1.
A random sample of 4,000 U.S. citizens was asked their opinion concerning gun control. A total of 2,600 of the 4,000 citizens in the sample stated that they are in favor of gun control legislation. Construct a 98% confidence interval for the true population proportion (p).
2.
An Animal Scientist wants to estimate the average weaning weight of the Hereford breed of beef cattle. Therefore, he selects a random sample of 100 Hereford calves and weighs them on the day they are weaned from their mothers. The sample mean for these 100 calves is 450 lb and the sample standard deviation is 50 lb. What is the point estimate of the mean of the entire population of all Hereford calves?
3.
The average litter size in Ohio is approximately 8 pigs per litter. Owners of a particular breed would like to prove that the mean litter size of their breed is greater than 8 pigs per litter. Therefore, they want to test:
Ho: = 8 pigs/litter
Ha: > 8 pigs/litter
They obtain a random sample of 100 litter size records from sows of this breed and find a sample mean of 8.4 pigs per litter and a sample standard deviation of 1 pig per litter. They decide to use a significance level of = 0.01.
What is the appropriate test statistic needed to test the null hypothesis?
4.
We want to test the following null and alternative hypotheses about a population proportion:
Ho: p = 0.70
Ha: p > 0.70
We observe 400 successes in a sample of 500 observations. Assume that it is valid to use large-sample procedures in this problem.
Calculate the test statistic needed to test the null hypothesis. Should we reject or not reject Ho: p = 0.70 if we use a significance level of = 0.05? Explain.
(2,529. 71274, 2,670.28726)Explanation / Answer
p is 2600/4000=0.65
N is 4000
z for 98% confidence is 2.33
thus the lower bound is p-z*sqrt(p*(1-p)/N)=0.65-2.33*sqrt(0.65*(1-0.65)/4000)=0.63243
upper bound is p+z*sqrt(p*(1-p)/N)=0.65+2.33*sqrt(0.65*(1-0.65)/4000)=0.66757
option D
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