. Previous studies have shown that in general female population approximately 32
ID: 3048697 • Letter: #
Question
. Previous studies have shown that in general female population approximately 32% of women deliver prematurely. Based on the data provided to 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).
Perterm 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: PPlacebo< PGeneral
Alternative hypothesis: PPlacebo > PGeneral
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a two-proportion z-test.
Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).
p = (p1 * n1 + p2 * n2) / (n1 + n2)
p = 0.25
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = 0.053033
z = (p1 - p2) / SE
z = 6.38
where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.
Since we have a one-tailed test, the P-value is the probability that the z-score is greater than 6.38.
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 have to reject the null hypothesis.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.