Take your survey data and code the gender question as Male=0 and Female=1. Suppo

Question

Take your survey data and code the gender question as Male=0 and Female=1. Suppose we hypothesize that women are more likely to respond to surveys than men are. Specifically, we believe that more than 55 percent of all respondents are women (this equates to the mean of the gender variable to be greater than 0.55). Use the methods learned this week to test this hypothesis. Survey data:   Male= 5    Females= 28

Present your results and discuss why you rejected, or failed to reject the null hypothesis.

Explanation / Answer

Solution:-

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

Null hypothesis: P < 0.55

Alternative hypothesis: P > 0.55

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the sample proportion 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 ]

= 0.087

z = (p - P) /

z = - 4.3

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 one-tailed test, the P-value is the probability that the z-score is less than - 4.3.

Thus, the P-value = less than 0.0001.

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we cannot accept the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that more than 55 percent of all respondents are women.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

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