4. RBI is analyzing the total credit flow in the economy and the circulation of money in the economy. In order to formulate its annual Monetary & Credit policy, RBI is assessing the credit off take in the banking sector and has classified as low, moderate and high, according to the total credit provided to various sectors of the economy. The total credit provided in Rs. During the four quarters of the calendar year is given below:
Credit Off take
(In Billion Rs.) Quarter
I II III IV
Low 18 10 7 5
Moderate 17 16 17 20
High 5 14 26 35
a. Is there a significant evidence in the above data to show that the Credit off take depend on the period. What is the rationale behind the choice of the test you would apply? Test at level of significance of 5%.
b. Also test whether the credit off take between the four quarters is significant. What is the rationale behind the choice of the test you would apply? Test at level of significance of 5%.
To analyze whether the credit off-take depends on the period (quarters) and whether the credit off-take between the four quarters is significant, we can use a statistical test called the chi-squared test for independence.
a. To test if the credit off-take depends on the period, we will conduct a chi-squared test for independence. The null hypothesis (H0) states that there is no association between the credit off-take and the period. The alternate hypothesis (Ha) suggests that there is an association between the credit off-take and the period.
The rationale behind choosing the chi-squared test for independence is that it examines whether two categorical variables are independent or influenced by each other. In this case, we have two categorical variables: credit off-take (low, moderate, and high) and the period (quarters I, II, III, and IV).
To apply the chi-squared test, we need to create a contingency table summarizing the observed frequencies of credit off-take and the period. The contingency table would look like this:
Quarter
I II III IV Total
Low 18 10 7 5 40
Moderate 17 16 17 20 70
High 5 14 26 35 80
Total 40 40 50 60 190
To calculate the expected frequencies, we assume the null hypothesis (H0) is true, i.e., there is no association between the credit off-take and the period. We then calculate the expected frequencies using the formula:
Expected frequency = (Sum of row total * Sum of column total) / Grand total
Using these expected frequencies, we can calculate the chi-squared test statistic:
Chi-squared test statistic = ∑ [(Observed frequency - Expected frequency)^2] / Expected frequency
We then compare this test statistic with the chi-squared distribution table at a significance level of 5% (with the appropriate degrees of freedom) to determine whether there is sufficient evidence to reject the null hypothesis.
b. To test whether the credit off-take between the four quarters is significant, we will again use the chi-squared test for independence. In this case, we will compare the observed frequencies of the credit off-take within each quarter.
The rationale behind choosing this test remains the same: it helps us determine if there is a significant association or dependency between the credit off-take and the quarters.
Again, we will create a contingency table for the observed frequencies within each quarter of the year. Calculate the expected frequencies assuming independence, and then use the chi-squared test statistic formula to determine if there is a significant association between the credit off-take and the quarters.
Remember, for both tests, we compare the test statistic to the chi-squared distribution table to make a decision regarding the null hypothesis.