[Banks' Tier 1 Leverage Ratio] The "Tier 1 Leverage Ratio" for banking companies is a

measure of bank risk, and is computed as tier 1 capital divided by average total consolidated

assets. Tier 1 capital is "core" capital-capital stock, undivided profits, and qualified preferred

stock, less intangibles. A sample of n = 51 banking companies was examined and the sample

mean Tier 1 Leverage Ratio was found to be 11.20% with a sample standard deviation of 3.32%.

Use this information to answer questions 1 to 12 below.

1) A 95% confidence interval for the population average Tier 1 Leverage Ratio (in percents) for

banking companies is given by which of the following?

(a) [4.693, 17.707]

(b) [4.532, 17.868]

(c) [10.266, 12.134]

(d) [10.289, 12.111]

2) Banking companies are receiving a lot of attention currently. Suppose forty different researchers

draw 40 different (and independent) samples of n = 51 banking companies and each constructs a

90% confidence interval for the (population) Tier 1 Leverage Ratio. How many of these confidence

intervals are expected to include the true value of the population average Tier 1 Leverage Ratio?

(a) 38

(b) 36

(c) 40, with 90% probability

(d) Can't answer with the information given

3)Using the same sample whose sample mean was 11.20% and sample standard deviation was 3.32%,

a confidence interval for a different level of confidence was constructed, and found to be [9.955,

12.445]. To what level of confidence does this interval correspond?

(a) 95%

(b) 98%

(c) 99%

(d) 100%

4) Which of the following ways of constructing a confidence interval will result in the smallest margin

Of error? Assume that the sample mean and sample standard deviation remain 11.20% and 3.32%,

respectively.

(a) using a 90% confidence level and a sample of 75 observations

(b) using a 90% confidence level and a sample of 150 observations

(c) using a 99% confidence level and a sample of 75 observations

(d) using a 99% confidence level and a sample of 300 observations

5) You re-check your sample and calculations used in question 8, and find that while the sample size

is n = 51 and sample mean is 11.20%, the actual sample standard deviation is higher than the

value of 3.32% used by you. If you re-compute the 95% confidence interval, how do you expect

this new confidence interval to compare with the confidence interval computed in question 8?

(a) The new confidence interval is smaller

(b) The new confidence interval has the same width

(c) The new confidence interval is larger

(d) It is impossible to say without more information