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 30**satisfy 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<

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