Question

recently conducted Gallup poll surveyed 1,485 randomly selected US adults and found that 48% of those polled approve of the job the Supreme Court is doing. The Gallup poll's margin of error for 95% confidence was given as ±5%. Students at the College of Idaho are interested in determining if the percentage of Yotes that approve of the job the Supreme Court is doing is different from 48%. They take a random sample of 30C of I students.

(a) Will a sample of size of 30satisfy the success-failure condition required for conducting inference on the proportion of Yotes that approve of the job the Supreme Court is doing?
Check if the success-failure condition required for constructing a confidence interval based on these data is met.
Success condition: np^=
Failure condition: n(1−p^)=
Are the conditions met?  ? NO YES

(b) Students correctly used inference to test H0:p=48% vs HA:p≠48% A pp-value of 0.038 was obtained. The appropriate conclusion for the hypothesis test at the 5% significance level is:
Since the p-value  ?  < > =  α
The students:
A. Fail to reject the null hypothesis
B. Reject the null hypothesis and accept the alternative

This means that:
A. There is statistically significant evidence, at the α=0.05 level, that the proportion of Yotes that approve of the job the Supreme Court is doing is 48% roughly 5% of the time.


B. There is not statistically significant evidence, at the α=0.05 level, that the proportion of Yotes that approve of the job the Supreme Court is doing is different from 48%.


C. There is statistically significant evidence, at the α=0.05 level, that the proportion of Yotes that approve of the job the Supreme Court is doing is different from 48%.

(c) The students collect a random sample of Yotes' opinions which yields 56% approving of the job the Supreme Court is doing. The computed margin of error is 4 .Assuming a 95% level, state the confidence interval for the percentage of Yotes that approve of the job the Supreme Court is doing.
  95% confidence interval: <p<

Answer 1