A researcher from the center invited a panel of 36 adults, 20 of whom have a 4-y
ID: 3323874 • Letter: A
Question
A researcher from the center invited a panel of 36 adults, 20 of whom have a 4-year college degree, to take part in a focus group. The researcher found that 4 of the 20 college-educated participants would avoid generic drugs at all cost, and the same sentiment was shared by 8 of the remaining 16 participants. Does the difference in education level plays a role in explaining the preference of brand-name drugs over their generic alternatives?
The distribution appropriate for modeling this problem?
Probability statement Excel command and the probability?
Do you think education plays a role in the brand-name drug preferences? Why?
What is PCF for College-educated participants?
What is PCF for non-college-educated participants?
What is the mean for college-educated participants?
What is the variance for non-college-educated participants?
Explanation / Answer
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: PCollege = PNoncolege
Alternative hypothesis: PCollege PNoncollege
Note that these hypotheses constitute a two-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.05. 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 = 0.3333
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = 0.15811
z = (p1 - p2) / SE
z = - 1.89
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 two-tailed test, the P-value is the probability that the z-score is less than - 1.89 or more than 1.89.
Thus, the P-value = 0.059
Interpret results. Since the P-value (0.059) is greater than the significance level (0.05), we have to accept the null hypothesis.
No the difference is not significant for preference of brand-name drugs over their generic alternatives
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