Question

13) A study published in 2008 in the American Journal of Health Promotion (Volume 22, Issue 6) by researchers at the University of Minnesota (U of M) found that 124 out of 1,923 U of M females had over $6,000 in credit card debt while 61 out of 1,236 males had over $6,000 in credit card debt.

a) Verify that the sample size is large enough in each group to use the normal distribution to construct a confidence interval for a difference in two proportions.

b) Construct a 95% confidence interval for the difference between the proportions of female and male University of Minnesota students who have more than $6,000 in credit card debt (pf - pm).

d) Does the interval contain the difference in sample proportions of female and male University of Minnesota students who have more than $6000 in credit card debt Phat_f - Phat_m ?

e) Explain why the previous question is silly and did not require you to even look at the interval.

f) According to your interval in (b) is it reasonable to assume that there is no difference between men and women at U of M regarding credit card debt? Clearly answer “yes” or “no.” ______ The briefly explain your answer? [3pt]

Answer 1

(a)

Group : females :

n1 = 1923

1= 124/1923 = 0.064

n11 = 1923 X 0.064 = 124 10

n1 (1 - 1) = 1923 X 0.936= 1800 10

So, both conditions are satisfied.

Group 2: Males:

n2 = 1236

2 = 61/1236 = 0.049

n22 = 1236 X 0.049 = 61 10

n2 (1 - 2) = 1236 X 0.951= 1175 10

Thus, it is Verifed that the sample size is large enough in each group to use the normal distribution to construct a confidence interval for a difference in two proportions.

(b)

= 0.05

From Table, critical values of Z = 1.96

Confidence Interval:

So,

Answer is:

(-0.001 0.031)

(d)

Yes, the interval contains the difference in sample proportions of female and male University of Minnesota students who have more than $6000 in credit card debt: -

(e)

The previous question is silly and did not require us to even look at the interval, because the confidence interval is constructed with the difference in sample proportions of female and male University of Minnesota students who have more than $6000 in credit card debt - , with Margin of Error on either side.

(f)

According to our interval in (b) it is reasonable to assume that there is no difference between men and women at U of M regarding credit card debt. Answer is “yes” Explanation: Since confidence interval is constructed with the difference in sample proportions of female and male University of Minnesota students who have more than $6000 in credit card debt obtained: (-0.001 0.031) includes 0, we conclude that there is no difference between men and women at U of M regarding credit card debt.