Question

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.

10. 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.

11. 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). Round your sample proportions and margin of error to four decimal places.

12. Test, at the 5% level, if there is evidence that the proportion of female students at U of M with more that $6,000 credit card debt is greater than the proportion of males at U of M with more than $6,000 credit card debt. Include all details of the test.

Answer 1

ANSWER::

(10)

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.

(11)

nf = 1923

= 124/1923 = 0.064

nm = 1236

= 61/1236 = 0.049

= 0.05

From Table, critical values of Z = 1.96

Confidence Interval:

So,

Answer is:

(-0.001, 0.031)

(12)

H0: Null Hypothesis: (The proportion of female students at the university with more than $6,000 credit card debt is not greater than Minnesota students who have more than $6,000 in credit card debt)

HA: Alternative Hypothesis: (The proportion of female students at the university with more than $6,000 credit card debt is greater than Minnesota students who have more than $6,000 in credit card debt) (Claim)

nf = 1923

= 124/1923 = 0.0645

nm = 1236

= 61/1236 = 0.0494

= 0.05

From Table, critical values of Z = 1.64

Pooled Proportion is given by:

Test Statistic is given by:

Since calculated value of Z = 1.767 is greater than critical value of Z = 1.64, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that the proportion of female students at the university with more than $6,000 credit card debt is greater than Minnesota students who have more than $6,000 in credit card debt.

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