11O personality preferences .M ers-Brigs: Marriage Counseling Most married coupl
ID: 3341209 • Letter: 1
Question
11O personality preferences .M ers-Brigs: Marriage Counseling Most married couples have two or three personality preferences in common (see reference in Problem t yers used a random sample of 375 married couples and found that 132 had three preferences in common. Another random sample of 571 couples showed that 217 had two personality preferences in common. Let pi be the popula- tion proportion of all married couples who have three personality preferences in common. Let p2 be the population proportion of all married couples who have two personality preferences in common. (a) Check Requirements Can a normal distribution be used to approximate the i p2 distribution? Explain. (b) Find a 90% confidence interval for pi-p2. (c) Interpretation Examine the confidence interval in part (a) and explain what it means in the context of this problem. Does the confidence interval contain all positive, all negative, or both positive and negative numbers? What does this tell you about the proportion of married couples with three personality preferences in common compared with the proportion of couples with two preferences in common (at the 90% confidence level)?Explanation / Answer
Sample 1 : Total sample size, n1 = 375 , married couple with three preferences in common = 132 so p1 = 132/375 = 0.352
Sample 2 : Total sample size, n2 = 571, married couple with two preferences in common = 217 so p2 = 217/571 = 0.38
(a) Yes, a normal distribution can be used to approximate the p1 - p2 distribution as the sampling distribution of a sample proportion is approximately normal (normal approximation of a binomial distribution) when the sample size is large enough and here sample size is large enough to use a normal approximation.
We often need to compare two treatments used on independent samples. We can compute the difference between the two sample proportions and compare it to the corresponding, approximately normal sampling distribution for p1 - p2
(b) 90% Confidence interval for p1 - p2 = (p1 - p2 )+- z.05 ( p1(1-p1)/n1 +p2(1-p2)/n2)0.5
= (0.352-0.38) +-1.6449( 0.352(1-0.352)/375 +0.38(1-0.38)/571)0.5
= (-0.08056 , 0.02456)
(c) The confidence interval contain both positive and negative number
In context of the problem it means that differece between two proportion is 0 and not statistically significant.
It means that at 10% significance level or 90% CI there is no difference between proportion of married couples with two or three preferences in common.
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