The Japanese harvester beetle has infected several forests in the Northwest. Official estimates are that 17% of trees are infected. You are a park ranger who has been seeing a lot of these beetles lately, and you think the rate is higher in your area. You check 400 trees around your cabin and find that 79 of them are infected.

• Go through the steps on the Hypothesis Test Guide (D2L). List each step like Step 1, Step 2, etc.
• Please check the conditions using complete sentences.
• Please do the calculations out the long way, but definitely use GeoGebra or a calculator stats package to check.
• Even if the conditions aren’t met, do the rest anyway.
• Use α = 0.03

PLEASE ANSWER PARTS A, C, AND D. Thank you!

2.2 For diagnostic testing, let X = true status (1 = disease, 2 = no disease) and Y = diagnosis (1 = positive, 2 = negative). Let πi = P (Y = 1|X = i), i = 1, 2.

a. Explain why sensitivity = π1 and specificity = 1 − π2.

c. For mammograms for detecting breast cancer, suppose γ = 0.01, sensitivity = 0.86, and specificity = 0.88. Given a positive test result, find the probability that the woman truly has breast cancer.

d. To better understand the answer in (c), find the joint probabilities for the 2 × 2 cross-classification of X and Y . Discuss their relative sizes in the two cells that refer to a positive test result.

In the casino version of the traditional Australian game of two-up, a spinner stands in a ring and tosses two coins into the air. The coins may land showing two heads, two tails, or one head and one tail (odds). Players can bet on either heads or tails at odds of one to one. Therefore, if a player bets $1 on heads, the player will win $1 if the coins land on heads but lose $1 if the coins land on tails. Alternatively, if a player bets $1 on tails, the player will win $1 if the coins land on tails but lose $1 if the coins land on heads. If the coins land on odds, all bets are frozen and the spinner tosses again until either heads or tails comes up. If five odds are tossed in a row all players lose.

(a) Construct the probability distribution respresenting the different outcomes that are possible for a $1 bet on heads.

(b) Construct the probability distribution respresenting the different outcomes that are possible for a $1 bet on tails.

(c) What is the expected long-run profit (or loss) to the player?

A researcher wanted to test the effectiveness of three different doses of medication on depression levels, so she recruited 60 people and split them evenly into the 3 groups. Below an ANOVA summary table from his hypothetical experiment. Use this table to answer questions below.

Using the information in the table (be sure to fill in, see other ANOVA table based essay question), test for significance (α=0.05). Please state the null hypothesis, research hypothesis, F obtained, F critical, df used, and conclusion of the study.

The random variable X represents the volatility of stocks in the S&P 500. The pdf of X is suspected to have the form:

f(x) = 4cxe^-(cx)^2, x > 0

Determine the value(s) of c so that the above function a valid probability density function

Suppose that a sample space consists of ? equally likely outcomes. Select all of the statements that must be true.

a. Each outcome in the sample space has equal probability of occurring.

b. Any two events in the sample space have equal probablity of occurring.

c. The probability of any event occurring is the number of ways the event can occur divided by ?.

d. Probabilities can be assigned to outcomes in any manner as long as the sum of probabilities of all outcomes in the sample space is 1.

The mean hourly wage for employees in goods-producing industries is currently $24.57 (Bureau of Labor Statistics website, April, 12, 2012). Suppose we take a sample of employees from the manufacturing industry to see if the mean hourly wage differs from the reported mean of $24.57 for the goods-producing industries. a. State the null hypotheses we should use to test whether the population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the goods-producing industries. 1. 2. 3. Choose correct answer from above choice State the alternative hypotheses we should use to test whether the population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the goods-producing industries. 1. 2. 3. Choose correct answer from above choice b. Suppose a sample of 30 employees from the manufacturing industry showed a sample mean of $23.89 per hour. Assume a population standard deviation of $2.40 per hour and compute the p-value. Round your answer to four decimal places. c. With = .05 as the level of significance, what is your conclusion? p-value .05, H 0. We that the population mean hourly wage for manufacturing workers the population mean of $24.57 for the goods-producing industries. d. Repeat the preceding hypothesis test using the critical value approach. Round your answer to two decimal places. Enter negative values as negative numbers. z = ; H 0

Suppose a "psychic" is being tested to determine if she is really psychic. A person in another room concentrates on one of five colored cards, and the psychic is asked to identify the color. Assume that the person is not psychic and is guessing on each trial. Define a success as "psychic identifies correct color". (a) What is p, the probability of success on a single trial? (show 1 decimal place) (b) If we conduct 10 trials, what is the probability that the psychic guesses zero or one of the colors correctly? (show 2 decimal places) (c) What is the mean or expected value of X, the number of correct answers out of 10 trials?

The following n = 10 observations are a sample from a normal population.

7.3    7.0    6.4    7.4    7.6    6.3    6.9    7.6    6.4    7.0

(a) Find the mean and standard deviation of these data. (Round your standard deviation to four decimal places.)

(b) Find a 99% upper one-sided confidence bound for the population mean μ. (Round your answer to three decimal places.)


(c) Test H₀: μ = 7.5 versus H_a: μ < 7.5. Use α = 0.01.

State the test statistic. (Round your answer to three decimal places.)

t =

State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.)

State the conclusion.

H₀ is rejected. There is insufficient evidence to conclude that the mean is less than 7.5.

H₀ is not rejected. There is sufficient evidence to conclude that the mean is less than 7.5.    

H₀ is not rejected. There is insufficient evidence to conclude that the mean is less than 7.5.

H₀ is rejected. There is sufficient evidence to conclude that the mean is less than 7.5.

(d) Do the results of part (b) support your conclusion in part (c)?

Yes

No   

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

Is fishing better from a boat or from the shore? Pyramid Lake is located on the Paiute Indian Reservation in Nevada. Presidents, movie stars, and people who just want to catch fish go to Pyramid Lake for really large cutthroat trout. Let row B represent hours per fish caught fishing from the shore, and let row A represent hours per fish caught using a boat. The following data are paired by month from October through April.

Use a 1% level of significance to test if there is a difference in the population mean hours per fish caught using a boat compared with fishing from the shore. (Let d = B − A.)

(a) What is the level of significance?

What is the value of the sample test statistic? (Round your answer to three decimal places.)

____________________________________

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

The western United States has a number of four-lane interstate highways that cut through long tracts of wilderness. To prevent car accidents with wild animals, the highways are bordered on both sides with 12-foot-high woven wire fences. Although the fences prevent accidents, they also disturb the winter migration pattern of many animals. To compensate for this disturbance, the highways have frequent wilderness underpasses designed for exclusive use by deer, elk, and other animals. In Colorado, there is a large group of deer that spend their summer months in a region on one side of a highway and survive the winter months in a lower region on the other side. To determine if the highway has disturbed deer migration to the winter feeding area, the following data were gathered on a random sample of 10 wilderness districts in the winter feeding area. Row B represents the average January deer count for a 5-year period before the highway was built, and row A represents the average January deer count for a 5-year period after the highway was built. The highway department claims that the January population has not changed. Test this claim against the claim that the January population has dropped. Use a 5% level of significance. Units used in the table are hundreds of deer. (Let d = B − A.)

(a) What is the level of significance?

What is the value of the sample test statistic? (Round your answer to three decimal places.)

Construct the confidence interval for the population mean

muμ.

cequals=0.980.98​,

x overbar equals 8.2x=8.2​,

sigmaσequals=0.90.9​,

and

nequals=5858

A

9898​%

confidence interval for

muμ

is

left parenthesis nothing comma nothing right parenthesis .,.

​(Round to two decimal places as​ needed.)

Answers are in bold under questions. I just need to know how to get them, so Please show work!!

A) If 25% of all vehicles at a certain emissions inspection failed the inspection. Assuming that successive vehicles pass or fail independently of one another. Calculate the following probabilities:

At least seven of the last 40 vehicles inspected failed.

0.9038

B) If 25% of all vehicles at a certain emissions inspection failed the inspection. Assuming that successive vehicles pass or fail independently of one another. Calculate the following probabilities:

In between 15 and 18 of the last 20 inspected passed

0.5929

C) If 25% of all vehicles at a certain emissions inspection failed the inspection. Assuming that successive vehicles pass or fail independently of one another. Calculate the following probabilities:

Given that less than 5 of the last 25 vehicles inspected failed, what is the probability that less than 3 of the 25 vehicles inspected failed?

0.1502

During a command staff meeting a presentation is being made regarding a study recently completed by a consultant on crime suppression strategies. This study was commissioned by the Mayor who is under political pressure to reduce the crime rate in your community. The study revealed that crime rates are reduced by several factors, as indicated in a multiple regression statistical model. The consultant presented the following table which includes each factor and its beta coefficient. During the meeting the Captain sitting next to you turns to you and whispers, “I can’t make heads or tails of this statistics stuff. Which factor appears to have the most effect on reducing the crime rate?” Answer the Captain’s question. Assume each of the following beta coefficients are statistically significant. Factor A .534 Factor B -.345 Factor C .893 Factor D -602