An article considered regressing y = 28-day standard-cured strength (psi) against x = accelerated strength (psi). Suppose the equation of the true regression line is  y = 1900 + 1.4x,

and that the standard deviation of the random deviation ϵ is 350 psi.

(a)

What is the probability that the observed value of 28-day strength will exceed 5000 psi when the value of accelerated strength is 2000? (Round your answer to four decimal places.)

(b)

What is the probability that the observed value of 28-day strength will exceed 5000 psi when the value of accelerated strength is 2500? (Round your answer to four decimal places.)

(c)

Consider making two independent observations on 28-day strength, the first for an accelerated strength of 2000 and the second for

x = 2500.

What is the probability that the second observation will exceed the first by more than 1000 psi? (Round your answer to four decimal places.)

(d)

Let Y₁ and Y₂ denote observations on 28-day strength when x = x₁ and x = x₂, respectively. By how much would x₂ have to exceed x₁ in order that P(Y₂ > Y₁) = 0.95?(Round your answer to two decimal places.)

In a survey of 1000 randomly selected adults in the United States, participants were asked what their most favorite and what their least favorite subject was when they were in school (Associated Press, August 17, 2005). In what might seem like a contradiction, math was chosen more often than any other subject in both categories! Math was chosen by 222 of the 1000 as the favorite subject, and it was also chosen by 362 of the 1000 as the least favorite subject.

(a) Construct a 95% confidence interval for the proportion of U.S. adults for whom math was the favorite subject in school. (Give the answers to four decimal places.)
(  ,  )

(b) Construct a 95% confidence interval for the proportion of U.S. adults for whom math was the least favorite subject. (Give the answers to four decimal places.)
(  ,  )

You may need to use the appropriate table in Appendix A to answer this question.

John Smith, a baseball player, throws three types of pitches; fastball (FB), curveball (CB) and slider (SL). He throws a fastball 45% of the time, a curveball 28% of the time, and a slider the rest of the time. About 72% of the fastballs are strikes, 70% of the curveballs are strikes, and only 32% of the sliders are strikes. Let S represent a strike and NS represent not a strike.

b) What is the probability (to 4 decimal places) that Smith throws a fastball and not a strike?

john Smith, a baseball player, throws three types of pitches; fastball (FB), curveball (CB) and slider (SL). He throws a fastball 45% of the time, a curveball 28% of the time, and a slider the rest of the time. About 72% of the fastballs are strikes, 70% of the curveballs are strikes, and only 32% of the sliders are strikes. Let S represent a strike and NS represent not a strike.

c) What is the probability (to 4 decimal places) that Smith throws a strike?

John Smith, a baseball player, throws three types of pitches; fastball (FB), curveball (CB) and slider (SL). He throws a fastball 45% of the time, a curveball 28% of the time, and a slider the rest of the time. About 72% of the fastballs are strikes, 70% of the curveballs are strikes, and only 32% of the sliders are strikes. Let S represent a strike and NS represent not a strike.

d) What is the probability (to 4 decimal places) that Smith throws a curveball given that it was a strike?

can somebody answer this question.

In a particular year, 68% of online courses taught at a system of community colleges were taught by full-time faculty. To test if 68% also represents a particular state's percent for full-time faculty teaching the online classes, a particular community college from that state was randomly selected for comparison. In that same year, 31 of the 44 online courses at this particular community college were taught by full-time faculty. Conduct a hypothesis test at the 5% level to determine if 68% represents the state in question.

Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

A. State the distribution to use for the test. (Round your standard deviation to four decimal places.)
P' ~ ________ (________,_________)

B. What is the test statistic? (Round your answer to two decimal places.)

C. What is the p-value? (Round your answer to four decimal places.)

D. Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.

(i) Alpha:
α =

E. Construct a 95% confidence interval for the true proportion. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your answers to four decimal places.)

A sample of 150 homes for sale in ABC City showed a mean asking price of $233,000, but the city claimed that the mean asking price for the population was $255,000. The population standard deviation of all homes for sale was $11,000. Use the p-value approach to conduct a full hypothesis test (all steps) that can be used to determine whether the mean asking price is significantly less than $255,000. Let α = .10.

During the recent primary elections, the democratic presidential candidate showed the following pre-election voter support in Alabama and Mississippi. State Voters Surveyed Voters in favor of Democratic Candidate Alabama 710 352 Mississippi 915 480 We want to determine whether or not the PROPORTIONS of voters favoring the Democratic candidate were the same in both states. In other words, is the first proportion (p1) the same as (p2)? What formula, from this week’s Notations and Symbols, would be applicable in the hypothesis test? (Notice you are not doing a hypothesis test – you are saying which formula applies).

Consider the following time series data.

a. develop the three-week moving average forecasts for this time series. Compute MSE and a forecast for week 7 (to 2 decimals if necessary).

b. use = 0.2 to compute the exponential smoothing forecasts for the time series. Compute MSE and a forecast for week 7 (to 2 decimals).

c. use a smoothing constant of =0.4 to compute the MSE (to 2 decimals).

How does significance level of a statistical test relate to our decision about whether an independent variable had an effect? How does our choice of significance level impact the likelihood of making a Type I and a Type II error? Be sure to thoroughly distinguish between the two types of errors.

College students are accumulating increasing amounts of debt while they pursue their degrees. This debt has a significant economic affect as the new graduates strive to begin their life after graduation. Nationally, the mean debt of recent graduates from all public 4-year institutions was $27995.

How does the loan debt of recent graduates of North Carolina's public colleges and universities compare to student loan debt nationally? To answer this question, use the data in this Excel file Student Debt Recent UNC System Grads that shows the student debt of recent graduates from 12 UNC System schools to perform the hypothesis test:

H₀: μ = 27995, H_a: μ < 27995

where μ is the mean student loan debt of all recent graduates from UNC System schools.

Question 1: What is the value of the test statistic t for this hypothesis test? (round x and s to the nearest whole number).

Question 2: What is the P-value for this hypothesis test? (use 4 decimal places in your answer)

Question 3: What is the correct conclusion for this hypothesis test?

a) The null hypothesis H₀: μ = 27995 is false with probability equal to the P-value, so reject H₀.

b) The null hypothesis H₀: μ = 27995 is true with probability equal to the P-value, so reject H₀.    

c) Reject the null hypothesis H₀: μ = 27995; the probability we have made a mistake is equal to the P-value.

d) Do not reject the null hypothesis H₀: μ = 27995 and conclude that the mean loan debt of recent UNC System graduates does not differ significantly from the national average.

e) Reject the null hypothesis H₀: μ = 27995 and conclude that the mean student loan debt of recent UNC System graduates is less than the national average.

Assuming that on average college students in the U.S. send 120 text messages per day. A researcher wants to examine if the amount of text messages sent daily by UNC students differs from the national average. The researcher took a sample of 64 UNC students, and finds that the mean number of texts per day is 126 with a standard deviation of 24. Use alpha .05

a) Is this a one-tail or two-tail test? Write appropriate hypotheses and assumptions.
b) Determine the degree of freedom and the critical value for this test.
c) Calculate the standard error.
d) Calculate the test statistics and determine its P-value.
e) State your conclusion by comparing the critical value to the test statistic and by comparing P to alpha.

Researchers at Johns Hopkins decide to use a case control study design to explore the association between women with breast cancer and DDT exposure. They interview women that have breast cancer undergoing chemo at the Johns Hopkins Hospital in Baltimore in 2014 and then take blood samples to test for DDT exposure. They also enroll a group of controls (without breast cancer) in the study based on patient lists at the hospital and also test them for DDT exposure. They find that that 360 of the women with breast cancer have DDT, exposure while 1,079 do not. Among the controls 432 have DDT exposure, and 2,446 do not.

A. Create an appropriate 2x2 table for this data.

B. Calculate the odds ratio comparing the odds of exposure for those with breast cancer to the odds of exposure for those without breast cancer (show work please)

C. Assume that this OR is significant. What does this OR mean (be specific using the context of this study)?

2. The inside diameters of bearings used in an aircraft landing gear assembly are known to
have a standard deviation of s = 0.002 cm. A random sample of 15 bearings has an
average inside diameter of 8.2535 cm.
a. Test the hypothesis that the mean inside bearing diameter is 8.25 cm. Use a two-
sided alternative and a = 0.05.
b. Find the P-value for this test.
c. Construct a 95% two-sided confidence interval on the mean bearing diameter
d. Repeat (a,b,c) above for a = 0.1. Compare with results for a = 0.05.
e. Repeat (a,b,c) above for a = 0.01. Compare with results for a = 0.05.

Hanna Frontier Software Solutions, Inc. (HFSI) has been investigating the possibility of developing a simulation software that can be used for analyzing risk and return from alternative lines of investment. The company is currently trying to decide between four proposed versions of the software: Simple (SS), Moderately Sophisticated (MSP), Sophisticated (SP), and Highly Sophisticated (HSP) versions of the software at respective development costs of $100,000, $200,000, $250,000, and $400,000.

• If the performance of the prototype developed by HFSI is better than existing software (a success), HFSI believes that it could sell the rights to its simulation software to a larger software developer for $250,000, $400,000, $650,000, and $880,000 for the SS, MSP,SP, and HSP versions, respectively.

• If the performance of the prototype developed by HFSI does not exceed the performance of the existing software (a failure), HFSI believes that it could still sell the rights to its simulation software to a larger software developer for $100,000, $130,000, $170,000, and $190,000 for the SS, MSP,SP, and HSP versions, respectively.

• HFSI estimates that the probability of a success for the software is 60%. However, the company also has the opportunity to hire a consultant who specializes in the study of markets for software. The consultant uses a market survey information to predict success or failure for software. In the past the consultant predicted a success for a prototype software in 85% of cases where the eventual product was a success. However, the consultant also predicted a success for the prototype in 25% of cases where the eventual product was a failure. The consultant’s fee for the service is $20,000.

1. What is the maximum amount HFSI should be willing to pay for a perfect forecast of success or failure for their software? Show the necessary steps. [2 points]
2. What is the maximum amount HFSI should be willing to pay for the consultant’s market survey information (EVSI)? On the basis of your findings, should the company hire the consultant? Show all the necessary steps. [7 points]

The data below show the number of injuries experienced by Gryffindor and Ravenclaw quidditch players during each game they played in the 2019 season: Gryffindor Ravenclaw

52 31

44 38

14 24

27 28

14 21

20 13

13 7

0 55

48 14

3 14

23 20

14 36

Do these data provide enough evidence to indicate that Gryffindor players experience more injuries than Ravenclaw players during a typical game from the 2018 season? Assume that the Gryffindor games and Ravenclaw games are independent samples. Use alpha = 0.05. Show your work and include a complete conclusion.