Question

A clinical trial is run to investigate the effectiveness of an experimental drug in reducing preterm delivery to a drug considered standard care and to a placebo. Pregnant women are enrolled and randomly assigned to receive either the experimental drug, the standard drug, or a placebo. Women are followed through delivery and classified as delivering preterm (< 37 weeks) or not. The data are shown below. Using this data, conduct the appropriate hypothesis test to assess if there a statistically significant difference in the proportions of women delivering preterm among the three treatment groups; running the test at a 5% level of significance.

            Table 1.

Preterm Delivery	Experimental Drug	Standard Drug	Placebo
Yes	17	23	35
No	83	77	65

1. Indicate the correct competing hypotheses:

1. The equation is supplied below, but indicate WHAT TYPE of Chi-square test you need to conduct: (1pt)

2. Indicate the decision rule:

Use the table below to help you compute the test statistic for problem #1.

            Table 2.

Preterm Delivery	Experimental Drug	Standard Drug	Placebo	Total
Yes
Observed	17	23	35
Expected
No
Observed	83	77	65
Expected
Total

1. Compute the test statistic and indicate the outcome: (7.5pts)
2. True or false: We DO NOT have statistically significant evidence at α=0.05 to show that intervention component and weight status are not independent. (1pt)

1. Indicate the most accurate p-value associated with the above-mentioned conclusion: (1pt)

Answer 1

Solution:-

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

Null hypothesis: The null hypothesis states that the pproportions of women delivering preterm among the three treatment groups are same.

H0: PExperimental Drug= PStanndard Drug= PPlacebo

Alternative hypothesis: At least one of the null hypothesis statements is false.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square test for homogeneity.

Analyze sample data. Applying the chi-square test for homogeneity to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

DF = (r - 1) * (c - 1) = (2 - 1) * (3 - 1)
D.F = 2
Er,c = (nr * nc) / n

?² = ? [ (Or,c - Er,c)² / Er,c ]
?² = 8.96

?²_Critical = 5.99

where DF is the degrees of freedom, r is the number of populations, c is the number of levels of the categorical variable, nr is the number of observations from population r, nc is the number of observations from level c of the categorical variable, n is the number of observations in the sample, Er,c is the expected frequency count in population r for level c, and Or,c is the observed frequency count in population r for level c.

The P-value is the probability that a chi-square statistic having 2 degrees of freedom is more extreme than 8.96.

We use the Chi-Square Distribution Calculator to find P(?² > 8.96) = 0.0113

Interpret results. Since the P-value (0.0113) is less than the significance level (0.05), we reject the null hypothesis.

From the aboove test we have sufficient evidence in the favor of the claim that there is significant difference in the proportions of women delivering preterm among the three treatment groups.