A sociologist is investigating the religious habits of women in a nearby city. S
ID: 3362396 • Letter: A
Question
A sociologist is investigating the religious habits of women in a nearby city. Specifically, she believes that the proportion of women in this city who regularly attend religious services is greater than 48%. A SRS of n = 320; indicated that 54.9 % were regular religious service attendants. H0: 0.48 Ha: > 0.48 A) The estimated true proportion of all women in the city who attend religious services is: 175.680 Incorrect: Your answer is incorrect. Note: express your answers to 3 decimal precision B) Based on this, the test statistic is: ztest = Note: express your answers to 3 decimal precision C) The P-value for this study is: P-value = Note: express your answers to 4 decimal precision
Explanation / Answer
Solution:-
a) The estimated true proportion of all women in the city who attend religious services = 0.549.
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P < 0.48
Alternative hypothesis: P > 0.48
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 ]
= 0.02793
z = (p - P) /
B) z = 2.471
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 more than 2.47.
C) Thus, the P-value = 0.0068
Interpret results. Since the P-value (0.0068) is less than the significance level (0.05), we cannot accept the null hypothesis.
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