Consider the following dataset taken for a field experiment (meansure in meters)

120 230 220 305 410 250 290 300 200 210 210 200 210 210 300 400 200 210 350 3000

a. Describe the distribution by computing:

i. Skweness. Interpret your result

ii. Kurtoisis. Interpret your result

b. is there an observation that may be an outlier? Explain?

Draw a boxplot for the distribution

Assume a bank with the following balance sheet at the end of the financial year.

Assets Amount Avg Duration (in years) Liabilities Amount Avg Duration (in years)

Reserves $100 0 Deposits $2000 1.5

T-notes $350 3 L T Debt $1000 15

Loans $1725 6 Equity $500 0

Mortgages $1325 12

Calculate the duration of assets and liabilities and the duration gap.

Assume a bank with the following balance sheet at the end of the financial year.

Assets Amount Avg Duration (in years) Liabilities Amount Avg Duration (in years)

Reserves $100 0 Deposits $2000 1.5

T-notes $350 3 L T Debt $1000 15

Loans $1725 6 Equity $500 0

Mortgages $1325 12

Calculate the duration of assets and liabilities and the duration gap.

Air enters the turbine of a gas turbine at 1400 kPa, 1400 K, and expands to 100 kPa in two stages. Between the stages, the air is reheated at a constant pressure of 350 kPa to 1400 K. The expansion through each turbine stage is isentropic.

Determine:

(b) the heat transfer for the reheat process, in kJ/kg of air flowing.

(c) the increase in net work as compared to a single stage of expansion with no reheat.

Exercise 3-16 (Static) Calculating ratios [LO3-8]

The 2021 balance sheet for Hallbrook Industries, Inc., is shown below.

The company’s 2021 income statement reported the following amounts ($ in thousands):

Required:
1. Calculate the current ratio. (Round your answer to 2 decimal places.)
2. Calculate the acid-test ratio. (Round your answer to 3 decimal places.)
3. Calculate the debt to equity ratio. (Round your answer to 2 decimal places.)
4. Calculate the times interest earned ratio. (Round your answer to 1 decimal place.)

Do female college students tend to weigh more or less than male college students, on average? Suppose that we use data from the Student Data sheet to help us make a decision about this question. We will assume that those who responded to the student data sheet are representative of all college students and are a random sample. Below are summary statistics from the student data sheet (rounded to the nearest integer):

a. Create a 95% confidence interval for the mean weight of all female college students

b. interpret the interval created in part a

c. create a 95% confidence interval for the mean weight of all male college students

d. interpret the interval created in part c

e. based on your interpretations of the confidence intervals above, do these data support any difference in average weight between female and male college students? Breifly justify your response.

A certain mutual fund invests in both U.S. and foreign markets. Let x be a random variable that represents the monthly percentage return for the fund. Assume x has mean μ = 1.7% and standard deviation σ = 0.7%.

(a) The fund has over 350 stocks that combine together to give the overall monthly percentage return x. We can consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all world stocks. Then we see that the overall monthly return x for the fund is itself an average return computed using all 350 stocks in the fund. Why would this indicate that x has an approximately normal distribution? Explain. Hint: See the discussion after Theorem 6.2.

(b) After 6 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? Hint: See Theorem 6.1, and assume that x has a normal distribution as based on part (a). (Round your answer to four decimal places.)


(c) After 2 years, what is the probability that x will be between 1% and 2%? (Round your answer to four decimal places.)

Suppose that a group of 700 smokers trying to quit were randomly selected to receive an antidepressant drug or a placebo for six weeks. Of the 350 patients who received the antidepressant drug, 162162 were not smoking one year later. Of the 350 patients who received the placebo, 102 were not smoking one year later.

Test the claim that antidepressants are effective in helping people to quit smoking at a significance level of α=0.05

(a) State the null and alternative hypotheses:
Let p1 be the proportion that were still not smoking from the antidepressant group, and p2p2 be the proportion that were still not smoking from the placebo group. Type either "=", ">", "<", or "not =".

H0:p1  p2 , H1:p1  p2

(b) The critical value is

(c) The test value is

(d) Based on our results, we
A. Do not reject H0
B. Reject H0

(e) The final conclusion is that
A. There is promising evidence to suggest that antidepressants can help people quit smoking.
B. There is not sufficient evidence to say that antidepressants can help people quit smoking.

Note: If rounding your calculations in between steps, please round to at least six decimal places of accuracy.

The lengths (in mm) of a sample of 100 largemouth bass are given in the file LargemouthBass.csv in Digital appendices. (You can find this file under the “Digital Appendices” link on Blackboard.) Use R construct a frequency distribution table and histogram of these data.