Question

A political poll finds that 305 out of 600 (50.8%) of a random sample of likely voters are in favor of the Democrat over the Republican prior to a recent local election between the two candidates. The p-value from a two-sided test of whether the population proportion is different than 50% is 0.714.

1. Which of the following could be the correct 95% confidence interval (range of plausible values) for the true proportion of voters that will vote for the Democrat candidate?

a. (46.8%, 54.8%)
b. (50.1%, 58.0%)
c. (53.0%, 61.0%)

2. When should you use the median as a summary statistic instead of the mean?

Answer 1

1)

Option A.(46.8%, 54.8%) is the correct Answer.

Since the Confidence Interval for the true proportion must contain or include ( p = 50% or 0.5 ), (46.8%, 54.8%) could be the correct 95% confidence interval (range of plausible values) for the true proportion of voters that will vote for the Democrat candidate.

2)

When a graph falls on a normal distribution, Using the mean is very good choice but when the data has extreme scores, then one should use the median instead of the mean.

Explanation:

Given the data in the question;

Null hypothesis H₀ : p = 50% or 0.5

Alternative hypothesis Hₐ : p ≠ 50% or 0.5

given that p-value = 0.714

The p-value is large, so we can not reject Null hypothesis.

Thus, p = 50% or 0.5

Meaning that, the Confidence Interval for the true proportion must contain or include ( p = 50% or 0.5 )

Thus, Option A.(46.8%, 54.8%) is the correct Answer.

Since the Confidence Interval for the true proportion must contain or include ( p = 50% or 0.5 ), (46.8%, 54.8%) could be the correct 95% confidence interval (range of plausible values) for the true proportion of voters that will vote for the Democrat candidate.

2)

When a graph falls on a normal distribution, Using the mean is very good choice but when the data has extreme scores, then one should use the median instead of the mean.