Derrick owns a farm in eastern North Carolina. A hurricane hit the area and destroyed a farm building and some farm equipment and damaged a barn. Item Adjusted Basis FMV before Damage FMV after Damage Insurance Proceeds Building $ 99,500 $ 142,000 $ 0 $ 57,000 Equipment 84,100 60,000 0 18,400 Barn 110,700 170,400 110,700 45,600 Due to the extensive damage throughout the area, the President of the United States declared all areas affected by the hurricane as a disaster area. Derrick, who files a joint return with his wife, had $50,400 of taxable income last year. Their taxable income for the current year is $166,200, excluding the loss from the hurricane. a-1. Calculate the amount of the loss deductible by Derrick and his wife. a-2. What amount of loss should be adjusted against current and last year?

According to Nielsen Media Research, the average number of hours of TV viewing by adults (18 and over) per week in the United States is 36.07 hours. Suppose the standard deviation is 8.6 hours and a random sample of 50 adults is taken. Appendix A Statistical Tables a. What is the probability that the sample average is more than 38 hours? b. What is the probability that the sample average is less than 38.5 hours? c. What is the probability that the sample average is less than 30 hours? If the sample average actually is less than 40 hours, what would it mean in terms of the Nielsen Media Research figures? d. Suppose the population standard deviation is unknown. If 66% of all sample means are greater than 35 hours and the population mean is still 36.07 hours, what is the value of the population standard deviation?

For each of the following exercises, define the appropriate parameter(s) and state the null and alternative
hypotheses.
Student Exercise 1 A water faucet manufacturer claims that the mean flow rate of a certain type of
faucet is less than 2.5 gallons per minute.

Student Exercise 2 Do males and females differ in terms of how many hours per week they exercise?

Student Exercise 3 Is the proportion of men who smoke cigarettes greater than the proportion of women who smoke cigarettes in the United States?

Student Exercise 4 In preschool, are the average weights of boys and girls different?

Student Exercise 5 A local grocery store claims that more than 53% of their customers use coupons.

Student Exercise 6 A medical researcher claims that less than 20% of American adults are allergic to a medication.

Identify the best graphics forms to illustrate the following data out of these choices: (Table, Bar chart, Line chart, Pie Chart, Flowchart, Organization Chart, Photograph Illustrations)
a. Potential new residential development project
b. Annual restaurant industry sales figures
c. Government unemployment data by industry and sector, in percentages
d. Figures showing the distribution of the H3N2 strain of type A flu virus in humans by
state
e. Figures showing the process of delivering water to a metropolitan area
f. LTE and 4G coverage in the United States, Canada, and Mexico
Figures showing what proportion of every state tax dollar is spent on education, social
services, transportation, debt, and other expenses
g.Academic, administrative, and operation divisions of a college, from the president to
department chairs and division managers
h.Figures comparing the sales of smartphones, tablets, and laptops over the past five
years

2. In 2016, the Centers for Disease Control and Prevention reported that 36.5% of adults in the United
States are obese. A county health service planning a new awareness campaign polls a random sample
of 750 adults living there. In this sample, 228 people were found to be obese based on their answers
to a health questionnaire. Do these responses provide strong evidence that the 36.5% figure is not
accurate for this region? Use a significance level of 5% to test your hypothesis.
a) Define the parameter of interest.
b) State the hypotheses statements.
c) Check that the conditions have been met and name the significance test to be used.
d) Perform the test and show all work.
e) Interpret the P-value and state your conclusion.
f) Calculate and interpret a 95% confidence interval.
g) Describe what a Type I and Type II error would be in the

0. The remaining problems will refer to the following table, which shows the average price of one gallon of gas in the United States over the past few weeks. (Data from ycharts.com/indicators/us gas price)

Date March 2 March 9 March 16 March 23 March 30

Price per gallon $2.514
$2.468
$2.343

$2.217 $2.103

6. Let f(t) be the price of one gallon of gas t days after February 29. (So, for example, the table shows that f(9) = 2.468.) Estimate f′(30).

7. Use your estimate to find the linearization of f(t) at t = 30.

8. Use your linearization to approximate the price for one gallon of gas on April 10.

9. Would it be reasonable to use your linearization to approximate the price of one gallon of gas on October 31? Why or why not?

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. More than a decade ago, high levels of lead in the blood put 89% of children at risk. A concerted effort was made to remove lead from the environment. Now, suppose only 10% of children in the United States are at risk of high blood-lead levels. (a) In a random sample of 206 children taken more than a decade ago, what is the probability that 50 or more had high blood-lead levels? (Round your answer to three decimal places.) Incorrect: Your answer is incorrect. (b) In a random sample of 206 children taken now, what is the probability that 50 or more have high blood-lead levels? (Round your answer to three decimal places.) Incorrect: Your answer is incorrect.

A typical coal-fired electric generating plant will burn about 3 metric tons of coal per hour.

Most of the coal burned in the United States contains 1 to 4 % by weight sulfur in the form of pyrite, which is oxidized as the coal burns:

4FeS₂(s) + 11 O₂(g) = 2 Fe₂O₃(s) + 8 SO₂(g)

Once in the atmosphere, the SO₂ is oxidized to SO₃, which then reacts with water in the atmosphere to form sulfuric acid:

SO₃(g) + H₂O(l) = H₂SO₄(aq)

If 61.8 metric tons of coal that contains 2.75 % by weight S is burned and all of the sulfuric acid that is formed rains down into a pond of dimensions 328 m x 200 m x 4.22 m, what is the pH of the pond? (OK to assume 2 mol H₃O⁺ per mole H₂SO₄.)

Hint: 1 metric ton = 1000 kg

Using survey data to calculate statistics can be extremely valuable, but you must also make sure that the sample and questions are unbiased. Design a pair of questions that are related to the same healthcare issue: one that is unbiased and another that would result in a bias in one direction or the other.  

Examples:

1. Do you think that the rate of type II diabetes diagnoses will increase over the next 10 years?
2. Given the large increase in childhood obesity in the United States, do you think that type II diabetes diagnoses will increase over the next 10 years?

Discuss why it is important to create a truly unbiased sample and survey questions. Then, look at your classmates' examples and comment on how their examples do or do not create a bias. Do not state which of your own questions is biased and which is unbiased. Your peers will determine which is which in their responses to you.