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.
In: Math
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.
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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?
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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.
Source |
SS |
df |
MS |
F |
Between |
(A) |
(C) |
(F) |
3.50 |
Within |
570 |
(D) |
(G) |
|
Total |
(B) |
(E) |
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.
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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
In: Math
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.
In: Math
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
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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?
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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.)
mean | |
standard deviation |
(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
Ha: 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.)
t > |
t < |
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
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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.
Oct | Nov | Dec | Jan | Feb | March | April | |
B: Shore | 1.7 | 1.9 | 2.0 | 3.2 | 3.9 | 3.6 | 3.3 |
A: Boat | 1.4 | 1.5 | 1.7 | 2.2 | 3.3 | 3.0 | 3.8 |
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.)
Wilderness District | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
B: Before highway | 10.1 | 7.4 | 12.7 | 5.6 | 17.4 | 9.9 | 20.5 | 16.2 | 18.9 | 11.6 |
A: After highway | 9.1 | 8.2 | 10.0 | 4.1 | 4.0 | 7.1 | 15.2 | 8.3 | 12.2 | 7.3 |
(a) What is the level of significance?
What is the value of the sample test statistic? (Round your
answer to three decimal places.)
In: Math
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.)
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57 61 57 57 58 57 61 54 68 51 49 64 50 48 65 52 56 46 54 49 51 47 55 55 54 42 51 56 55 51 54 51 60 62 43 55 56 61 52 69 64 46 54 47
Create a frequency table using the data above
Use 7 classes
Show the relative and cumulative frequencies
List the class boundaries and class mid-points
What is the modal class?
In: Math
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
In: Math
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
In: Math
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In: Math