Question

Two random samples of student loans were collected: one from students at for-profit schools and another from students at non-profit schools. The accompanying data show the sample sizes and the number of loans in each sample that defaulted. Complete parts a through c. Click the icon to view the loan data. a. Perform a hypothesis test using a = 0.10 to determine if the proportion of for-profit loans that default is larger than the proportion of loans for nonprofit schools that default. Let P, represent the population proportion of loans for for-profit schools that default and let P2 represent the population proportion of loans for nonprofit schools that default. Identify the null and alternative hypotheses. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals. Do not round.) O A. Ho: P1 - P2 OB. Ho: P: - P2? OC. Ho: P1 - P2* Hy : P1 - P2 Hy:P1-P25 H: P1 - P2 D. Ho: P1 - P2 OE. Ho: P1 - P22 OF. Ho: P4-P25 HP - P22 HP - P2 H: P1-P2> Identify the test statistic. (Round to two decimal places as needed.) Identify the critical value. (Round to two decimal places as needed.) Click to select your answer(s).

Answer 1

= = = From the given information, for Profit: X =25,^, =265, for Non Profit: X2=13, and >,=235. 25 sample proportions P1 = 0.0943, X, _ 13 P2 -0.0553 12 265 235 The point estimate for the difference of proportions is P1-P2 = 0.0943-0.0553 = 0.0390. (a) Answer: F. Null hypothesis H.: A-250 Alternative hypothesis : P->0 X+X, 25+13 Pooled proportion P= 0.0760,Q=1-P=1-0.0760 = 0.924. m+na 265+235 Level of significance a=0.10, then the critical value is 20.10 = 1.28 Pi-P2 0.0943-0.0553 Test statistic Zca == 1.6425 1 (0.076x0.924) 12 265 235 The value of the test statistic greater than the critical value, it falls in the rejection region, we reject the null hypothesis. Reject the null hypothesis. There is sufficient evidence to conclude that the proportion of for-profit loans that default is larger than the proportion of loans for nonprofit schools that default. (b) P-value: P(Z 21.64) = 0.0505 The P-value is less than the alpha level of a=0.10. Therefore we reject the null hypothesis. This conclusion coincides with the conclusion made in part a. (C)100(1-)% confidence interval for difference difference in the true proportions is —+- (0.076 (2-pa)=znyfo(4)(21py) +2.ng/20 ( + ) 90% confidence interval to estimate the difference in the proportion of loans in default in the given two types of schools is -(00 1 = 0.039-1.645, (0.076x0.924) 10.07620 924)( 265 * 235 0.039+1.645, +1.645, 10.076~0.924) (265 +235) =(-0.0001,0.0781) The confidence interval has a lower limit of -0.0001 and an upper limit of 0.0781.