A random sample of 100 people was taken. Eighty-five of the people in the sample

Question

A random sample of 100 people was taken. Eighty-five of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly different than 0.8.

At 95% confidence, it can be concluded that the proportion of the population in favor of candidate A...?

a) is definitely equal to 0.8

b) is definitely not equal to 0.8

c) could be equal to 0.8. The sample does not provide definitive evidence that it is not 0.8.

d) is 0.85 because that is the proportion in the sample, which is taken randomly.

Explanation / Answer

Solution:- At 95% confidence, it can be concluded that the proportion of the population in favor of candidate (c) could be equal to 0.8. The sample does not provide definitive evidence that it is not 0.8.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P = 0.80

Alternative hypothesis: P 0.80

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample proportion is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).

= sqrt[ P * ( 1 - P ) / n ]

= 0.04

z = (p - P) /

z = 1.25

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the z-score is less than 1.25 or greater than 1.25.

Thus, the P-value = 0.1056 + 0.1056

Interpret results. Since the P-value (0.2112) is greater than the significance level (0.05), we cannot reject the null hypothesis.

At 95% confidence, it can be concluded that the proportion of the population in favor of candidate (c) could be equal to 0.8. The sample does not provide definitive evidence that it is not 0.8.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.