- 2nd Nov 2021
- 06:03 am
Problem A1:
Data Scenario #2, Question 1: Which policy more effectively discourages delinquency, Credit Card A or Credit Card B?
1. The hypotheses are the following:
H A : p? - p? > 0
H?: p? - p? ? 0
The significance level is 5%.
2. The P-value < 0>
3. Because the P-value is less than the significance level of 5%, we reject the null hypothesis. The difference in proportions was statistically significant, z = 6.32, p < 0>
4. Proportion of Credit Card A customers who are delinquent was greater than the proportion of Credit Card B customers who are delinquent. Credit Card B outperforms Card A.
Problem A2:
Data Scenario #2, Question 2: Even if Credit Card B more effectively discourages delinquency, is it worth the extra cost to Capital One compared to Credit Card A?
1. The hypotheses are the following:
H A : p? - p? > 0.10
H?: p? - p? ? 0.10
The significance level is 5%.
2. The P-value is 0.008
3. Because the P-value is less than the significance level of 5%, we reject the null hypothesis. The test was significant, z = 2.42, p = 0.008.
4. The difference in proportions were significantly greater than 0.10. It is worth the extra cost to Capital One compared to Credit Card A.
Problem A3:
Data Scenario #3, Question 1: Which policy more effectively discourages delinquency, Credit Card A or Credit Card B?
1. The hypotheses are the following:
H A : p? - p? > 0
H?: p? - p? ? 0
The significance level is 5%.
2. The P-value < 0>
3. Because the P-value is less than the significance level of 5%, we reject the null hypothesis. The difference in proportions was statistically significant, z = 3.59, p < 0>
4. Proportion of Credit Card A customers who are delinquent was greater than the proportion of Credit Card B customers who are delinquent. Credit Card B outperforms Card A.
Problem A4:
Data Scenario #3, Question 2: Even if Credit Card B more effectively discourages delinquency, is it worth the extra cost to Capital One compared to Credit Card A?
1. The hypotheses are the following:
H A : p? - p? > 0.10
H?: p? - p? ? 0.10
The significance level is 5%.
2. The P-value is 0.656
3. Because the P-value is greater than the significance level of 5%, we fail to reject the null hypothesis. The test was not significant, z = -0.40, p = 0.656.
4. The difference in proportions was not significantly greater than 0.10. It is not worth the extra cost to Capital One compared to Credit Card A.
Problem B1:
Data Scenario #1, Question 3: Is the delinquency rate for Credit Card A lower than the historical delinquency rate of 30%?
1. The hypotheses are the following:
H A : p? < 0> H?: p? ? 0.30
The significance level is 5%.
2. The P-value < 0>
3. Because the P-value is less than the significance level of 5%, we reject the null hypothesis. The proportion of all Credit Card A customers who are delinquent was significantly less than 0.30, z = -7.81, p < 0>
4. The delinquency rate for Credit Card A is lower than the historical delinquency rate of 30%.
Problem B2:
Data Scenario #2, Question 3: Is the delinquency rate for Credit Card A lower than the historical delinquency rate of 30%?
1. The hypotheses are the following:
H A : p? < 0> H?: p? ? 0.30
The significance level is 5%.
2. The P-value = 0.165.
3. Because the P-value is greater than the significance level of 5%, we fail to reject the null hypothesis. There is insufficient evidence to reject the claim that the delinquency rate for Credit Card A lower than the historical delinquency rate of 30%, z = -0.98, p = 0.165
4. The delinquency rate for Credit Card A is greater than the historical delinquency rate of 30%.
Problem B3:
Data Scenario #3, Question 3: Is the delinquency rate for Credit Card A lower than the historical delinquency rate of 30%?
1. The hypotheses are the following:
H A : p? < 0> H?: p? ? 0.30
The significance level is 5%.
2. The P-value = 0.002
3. Because the P-value is less than the significance level of 5%, we reject the null hypothesis. The proportion of all Credit Card A customers who are delinquent was significantly less than 0.30, z = -2.93, p = 0.002.
4. The delinquency rate for Credit Card A is lower than the historical delinquency rate of 30%.
