A gay rights activist thinks that if Americans believe homosexuality is not chos

Question

A gay rights activist thinks that if Americans believe homosexuality is not chosen, the majority of them will then consider homosexuality an acceptable lifestyle. To test this, he asks a sample of Americans whether they believe homosexuality is chosen and whether they consider it an acceptable lifestyle. Out of 178 who believe homosexuality is not chosen, 101 say they consider it an acceptable lifestyle. (Data simulated from Schmalz, 1993.) Can we conclude at the 0.05 level of significance that the gay activist's belief is true? 4.

Explanation / Answer

Solution:-

4)

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

Null hypothesis: P < 0.50
Alternative hypothesis: P > 0.50

Note that these hypotheses constitute a one-tailed test.

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 (S.D) and compute the z-score test statistic (z).

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

S.D = 0.03748
z = (p - P) / S.D

z = 1.799

zcritical = 1.645

Rejection region is z > 1.645

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 greater than 1.799.

Thus, the P-value = 0.036

Interpret results. Since the P-value (0.036) 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 the gay's activist's beleif is true.

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