hree percent of a man's body is essential fat; for a woman the percentage is closer to 12.5%. As the name implies, essential fat is necessary for a normal healthy body. Fat is stored in small amounts throughout the body. Too much fat, however, can be dangerous to your health. For men between 18 and 39 years old, a healthy percent of body fat ranges from 8% to 19%; for women of the same age, it's 21% to 32%. Measuring body fat can be tedious and expensive. The "standard reference" measurement is by dual-eneregy X-ray absorptiometry (DEXA), which involves two low-dose X-ray generators and takes from 10 to 20 minutes. Because of the time and expense involved with the DEXA method, health professionals would like to be able to make a useable prediction of body fat from easily measurable variables such as weight or waist size.

1) Determine the 99% confidence interval for the slope of the least squares regression line of %body fat on waist size.

2) Determine a 99% confidence interval for the mean %body fat found in people with 40-inch waists (use 2 decimal places).

3) Determine a 99% prediction interval for the %body fat of an individual with a 40-inch waist (use 2 decimal places).

2. Using the SCC men’s/women’s class sample data at the ?=0.05, is there enough evidence to conclude that there is a significant linear correlation between men’s/women’s height and men’s/women’s shoe size?

a. State the null and alternate hypotheses.

b. Specify the level of significance.

c. State the correlation coefficient. (3 decimal places)

d. State the critical value from Table 11. (Use the value of n that is closest to your sample size.)

e. State whether to “reject the ?0” or “fail to reject the ?0”.

f. Interpret the decision in the context of the original claim

Find the 25th, 50th, and 75th percentile from the following list of 32 data

(a) Food Dragon and Delivery Woo are two main food delivery companies in Hong Kong. Suppose the delivery time of these two companies both follow a normal distribution. A random sample of size 10 is selected from each of the food deliveries.

Sample Size mean(mins) standard deviation(mins)

Food Dragon 10 20 5

Delivery Woo 10 15   6

Assuming the delivery times of both companies are normal with equal variances, find the 90% confidence interval for the difference between the mean delivery time of Food Dragon and Delivery Woo. [8marks]

(b) A random sample of 1000 citizens from Macau have been tested for the anti-body for the coronavirus. It was found that 150 of these citizens has the anti-body for the coronavirus. Find a 93% confidence interval for the true population proportion of citizens in the Macau with the anti-body. [5 marks]

(c) An engineer wants to find out the concentration of carbon monoxide (µg/m³ ) emitted by a newly invented car. The engineer collected 14 observations in a randomly chosen period.

68, 54, 32, 80, 50, 40, 60, 60, 55, 40, 42, 50, 60, 43

Construct a 95% confidence interval for the mean concentration of carbon monoxide. Assume that the concentrations of CO are normally distributed. [7 marks]

At the end of the year, a company offered to buy 4,450 units of a product from X Company for a special price of $11.00 each instead of the company's regular price of $17.00 each. The following information relates to the 62,400 units of the product that X Company made and sold to its regular customers during the year:

Fixed cost of goods sold for the year were $142,272, and fixed period costs were $83,616. Variable period costs include selling commissions equal to 3% of revenue.

6. Profit on the special order is

7. Assume the following two changes for the special order: 1) variable cost of goods sold will decrease by $0.78 per unit, and 2) there will be no selling commissions. What would be the effect of these two changes on the special order profit?

8. There is concern that regular customers will find out about the special order, and X Company's regular sales will fall by 950 units. As a result of these lost sales, X Company's profits would fall by

Part 3:

In Module 3, we looked at the hours of sleep that FTCC students get each night. I found online that the average hours of sleep that an adult gets is 6.8 hours. Does this seem likely based on our sample of students? You should show all work supporting this claim and write a paragraph explaining your decision.

You can use Intervals or Hypothesis testing to prove or disprove this claim. You will choose the confidence level or significance level.

Show all steps in the chosen process.

If you do a hypothesis test, include the claim, hypothesis, significance level, so on…

If you do an interval, give confidence level, margin of error, so on…

Explain your reasoning in detail. Why do you think that the average is 6.8 hours or not 6.8 hours? Back up your opinion using the statistical information.

You should write one paragraph explaining the results of your statistical process.

Part 4:

In Module 3, we looked at the GPAs of FTCC students. I found online source that claims the average GPA of college students in the US is 3.11. Does this seem likely based on our sample of students? You should show all work supporting this claim and write a paragraph explaining your decision.

You can use Intervals or Hypothesis testing to prove or disprove this claim. You will choose the confidence level or significance level.

Show all steps in the chosen process.

If you do a hypothesis test, include the claim, hypothesis, significance level, so on…

If you do an interval, give confidence level, margin of error, so on…

Explain your reasoning in detail. Why do you think that the average GPA is 3.11 or is not 3.11? Back up your opinion using the statistical information.

You should write one paragraph explaining the results of your statistical process.

1. The finance manager for Widget Inc. would like to analyze the following sales data for Widget Inc.in 2012.  

1. Calculate two statistics that measure variability.  What do these statistics tell us about the data?
2. Calculate two statistics that measure central tendency.  What do these statistics tell us about the data?
3. Create a frequency distribution of the sales data.  (Include all five columns in your frequency distribution).
4. Find the 80^th percentile.  What does this number represent?

1. Frank Rizzo is considering two investment  options with seven-year lives. Option one pays $250 every quarter, the other pays $500 semi-annually. The option with the better value would be:
A. $250 every quarter.
B. Both options are equally attractive.
C. $500 semi-annually.

2. Darius Rucker is leaving Theta Tech after several years. During his time at Theta he accumulated a deferred payroll benefit.  He must choose between a lump-sum distribution or annual payments over the next 10 years, with his first payment deposited today. He believes he can invest any sum received at 5.15% for the next ten years. The annual payments are  $12,500 and the lump-sum distribution is $105,000. To the nearest dollar, the more valuable choice is:
A. The annual payments.
B. The lump-sum distribution.
C. Both choices have the same value.