Previous studies have shown that in general female population approximately 32%
ID: 3049445 • Letter: P
Question
Previous studies have shown that in general female population approximately 32% of women deliver prematurely. Based on the data provided below you need to assess whether the proportion of women delivering prematurely is significantly higher in the placebo group compared with the general female population. Run the test at a 5% level of significance, and report your test statistic value. (round to 2 decimal places).
Preterm Delivery . experimental Drug Standard Drug placebo
yes 17 23 35
no 83 77 65
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P < 0.32
Alternative hypothesis: P > 0.32
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 ]
= 0.046648
z = (p - P) /
z = 0.64
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 0.64.
Thus, the P-value = 0.2611
Interpret results. Since the P-value (0.2611) is greater than the significance level (0.05), we have to accept the null hypothesis.
Hence we do not have sufficient evidence in the favor of the claim that proportion of women delivering prematurely is significantly higher in the placebo group compared with the general female population.
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