# The bad debt ratio for a financial institution is defined to be the dollar value of loans defaulted divided by the total dollar value of all loans made.

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1) The bad debt ratio for a financial institution is defined to be the dollar value of loans defaulted divided by the total dollar value of all loans made. Suppose that a random sample of seven Ohio banks is selected and that the bad debt rations (written as percentages) for these banks are 7%, 4%, 6%, 7%, 5%, 4% , and 9%. Assuming the bad debt ratios are approximately normally distributed, the Mega stat output of a 95% confidence interval for the mean bad debt ratio of all Ohio banks is as follows:

Confidence level 95%

Mean 6

Std. deviation 1.826

N 7

T(df=6) 2.447

Half width - 1.689

Upper confidence limit 7.689

Lower confidence limit 4.311

a. What is the 95% confidence interval for the true mean bad debt ratio of all Ohio banks?

b. Banking officials claim the mean bad debt ratio for Ohio banks is higher that the mean bad debt ratio for all banks in the Midwest region. The Midwest region bad debt ratio is known to be 3.5 percent. Using the 95 percent confidence interval, can we be confident that the banking officals' claim is true? Explain

2)To see if young men ages 8 through 17 years spend more or less than the national average of $24.44 per shopping trip to a local mall, the manger surveyed 33 young men and found the average amount spent per visit was $22.67. The population standard deviation is known to be $3.70. At alpha = 0.02, can it be concluded that the average amount spent by all young men at the local mall is not equal to the national average of $24.44?

Perform an appropriate hypothesis test. Be sure to state the null and alternate hypothesis, and provide sufficient justification for your decision.

2) The bad debt ratio for a financial institution is defined to be the dollar value of loans defaulted divided by the total dollar value of all loans made. Suppose that a random sample of seven Ohio banks is selected and that the bad debt rations (written as percentage) for these banks are 7%, 4%, 6%, 7%, 5%, 4%, and 9%. The bad debt ratios appear to be normal distributed. Below is the mega stat output.

3.50 hypothesized value

6.00 mean bad debt ratio

1.83 std deviation

0.69 std. error

7 n

6 df

3.62 t value

.055 p value (one tail upper)

a. what are the null and alternate hypothesis?

b. Use the p-value to test this hypothesis by setting alpha equal to 0.05. what do you conclude

c. How much evidence is there that the mean bad debt ratio for Ohio banks exceeds 3.5%?

3) The average waiting time per customer at a fast food restaurant has been 7.5 minutes. The customer waiting time has a normal distribution. The manager claims that the use of a new cashier system will decrease the average customer waiting time in the store. A random sample of 250 customer transactions has been recorded. AT a significance level of .05, what is the z-value rejection point condition? That is we reject the null hypothesis if: Pick one

Z<-1.645

Z>1.645

Z>1.96

Z<-1.96

Z<-2.33

4) A new company is in the process of evaluating its customer service. The company offers two types of sales 1) internet sales 2) store sales. The marketing research manager believes that monthly mean internet sales are more than monthly mean store sales. The null hypothesis for this problem would be stated:

Mean internet - mean store >0

Mean internet - mean store <0

Mean internet - mean store > or equal to 0

Mean internet - mean store <or equal to 0

Mean internet - mean store =0

https://brainmass.com/statistics/hypothesis-testing/157316

#### Solution Summary

The bad debt ratio for a financial institution is defined to be the dollar value of loans defaulted divided by the total dollar value of all loans made. Suppose that a random sample of seven Ohio banks is selected and that the bad debt rations (written as percentages) for these banks are 7%, 4%, 6%, 7%, 5%, 4% , and 9%. Assuming the bad debt ratios are approximately normally distributed, the Mega stat output of a 95% confidence interval for the mean bad debt ratio of all Ohio banks is as follows: