American football is the highest paying sport on a per-game basis. The quarterback, considered the most important player on the team, is appropriately compensated. A sports statistician wants to use 2009 data to estimate a multiple linear regression model that links the quarterback’s salary (in $ millions) with his pass completion percentage (PCT), total touchdowns scored (TD), and his age. A portion of the data is shown in the accompanying table. Name Salary PCT TD Age Philip Rivers 25.5566 65.2 28 27 Jay Cutler 22.0441 60.5 27 26 ⋮ ⋮ ⋮ ⋮ ⋮ Tony Romo 0.6260 63.1 26 29

c. Drew Brees earned 12.9895 million dollars in 2009. What is his predicted salary if PCT = 70.6, TD = 34, and Age = 30? (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.) Salaryˆ

d. Tom Brady earned 8.0073 million dollars in 2009. According to the model, what is his predicted salary if PCT = 65.7, TD = 28, and Age = 32? (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.) Salaryˆ e-1. Compute the residual salary for Drew Brees and Tom Brady. (Negative values should be indicated by a minus sign. Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

In problems 1 – 5, a binomial experiment is conducted with the given parameters. Compute the probability of X successes in the n independent trials of the experiment.

1.         n = 10, p = 0.4, X = 3

2.         n = 40, p = 0.9, X = 38

3.         n = 8, p = 0.8, X = 3

4.         n = 9, p = 0.2, X < 3

5.         n = 7, p = 0.5, X = > 3

According to American Airlines, its flight 1669 from Newark to Charlotte is on time 90% of the time. Suppose 15 flight are randomly selected and the number of on – time flights is recorded.

            a.         Find the probability that exactly 14 flights are on time.

            b.         Find the probability that at least 14 flights are on time.

            c.          Find the probability that fewer than 14 flights are on time.

            d.         Find the probability that between 12 and 14 flights are on time.

            e.         Find the probability that every flight is on time.

The quarterly returns for a group of 53 mutual funds with a mean of 2.1​% and a standard deviation of 5.1​% can be modeled by a Normal model. Based on the model ​N(0.021​,0.051​), what are the cutoff values for the ​

a) highest 10​% of these​ funds? ​
b) lowest 20​%?
​c) middle 40​%?
​d) highest 80​%?

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean u=266 and standard deviation 26 days. (a) what is the probability that a randomly selected pregnancy lasts less than 256 days? (b) what is the probability that a random sample of 16 preganacies has a mean geatation period of 256 days or less? (c) what is the probability that a random sample of 37 preganacies has a mean geatation period of 256 days or less? MUST SHOW WORK

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 130 millimeters, and a standard deviation of 6 millimeters. If a random sample of 33 steel bolts is selected, what is the probability that the sample mean would be greater than 130.6 millimeters? Round your answer to four decimal places.

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 9.7 hours and a random sample of 52 adults is taken.

a. What is the probability that the sample average is more than 35 hours?

b. What is the probability that the sample average is less than 38.8 hours?

c. What is the probability that the sample average is less than 29 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 75% of all sample means are greater than 48 hours and the population mean is still 36.07 hours, what is the value of the population standard deviation?

The contents of bottles of beer are Normally distributed with a mean of 300 ml and a standard deviation of 5 ml.

What is the probability that the average contents of a six-pack will be between 293 ml and 307 ml?

1. Murphy’s Law, a pub in downtown Rochester, claims its patrons average 25 years of age. A random sample of 40 bar patrons is taken and their mean age is found to be 26.6 years with a standard deviation of 4.5 years. Do we have enough evidence to conclude at the level of significance α = 0.025 that, on average, patrons at Murphy’s Law are older than 25?

Determine the test statistic.

Determine the range of P-values.

Write your decision and explain how you reached it.

Write the conclusion that addresses the original claim.

Determine the type of error you could have made and explain why. (Type I or Type II

error)

2. The coffee machine at your company has been acting weirdly these past few days. You were assured that the machine would pour 7 ounces of coffee every time you press the button. You believe that this is not true anymore and want to call the technician. Before you do so, you gather a sample of 15 coffees and find out that the mean amount of coffee in each cup is 6.8 ounces with a standard deviation of 1 ounce. Is there sufficient evidence to show that the population mean is different than 7 ounces? Perform a test at the 0.05 level of significance. Assume normality.

Determine the test statistic.

Determine the range of P-values.

Write your decision and explain how you reached it.

Write the conclusion that addresses the original claim.

Determine the type of error you could have made and explain why. (Type I or Type II

error)

A well-designed questionnaire should meet the research objectives. Give examples of preparatory work that one should conduct to ensure that these objectives are met.

The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of a village are shown below.

Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: The distributions are different.
H₁: The distributions are different.H₀: The distributions are the same.
H₁: The distributions are the same.    H₀: The distributions are different.
H₁: The distributions are the same.H₀: The distributions are the same.
H₁: The distributions are different.

(b) Find the value of the chi-square statistic for the sample. (Round your answer to three decimal places.)


Are all the expected frequencies greater than 5?

YesNo    

What sampling distribution will you use?

uniformStudent's t    binomialnormalchi-square

What are the degrees of freedom?


(c) Estimate the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?

Since the P-value > α, we fail to reject the null hypothesis.Since the P-value > α, we reject the null hypothesis.    Since the P-value ≤ α, we reject the null hypothesis.Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, the evidence is insufficient to conclude that the village population does not fit the general Canadian population.At the 5% level of significance, the evidence is sufficient to conclude that the village population does not fit the general Canadian population.   

2. We are interested in analyzing data related to the Olympics from one decade. We are looking at individuals and if they participated in the summer or winter Olympics and whether or not they won a medal. Use S to denote summer and M to denote if a medal was won. The probability that someone participated in the summer Olympics is 72%. The probability that they won a medal is 13%. The probability that they won a medal and it was in the summer Olympics is 10%. ( please show steps)

a. What percentage of people participated in the summer Olympics or won a medal?

b. What percentage of people participated in the winter Olympics?

c. Given someone won a medal, what is the probability that they participated in the summer Olympics?

d. What percentage of people did NOT participate in the summer games NOR won a medal?

e. Are M and S mutually exclusive events? Why or why not? f. Are M and S independent events? Explain, using probabilities.

g. If we know someone participated in the summer Olympics, what is the probability that they also won a medal?

A) Find the upper limit for the mean at the 90% confidence level.

B) Find the lower limit for the mean at the 90% confidence level.

C) Find the width of the confidence interval at the 90% confidence level.

D) Find the score from the appropriate probability table (standard normal distribution, t distribution, chi-square) to construct a 99% confidence interval.

If you use Excel, please list what Excel functions would allow me to get this answers for future reference

Question 1:

Eight measurements were made on the inside diameter of forged piston rings used in an automobile engine. The data (in millimeters) are 74.001, 74.003, 74.015, 74.000, 74.005, 74.002, 74.005, and 74.004.

1. Compute the sample mean and sample standard deviation of the temperature data.
2. Graph a histogram of the data.
3. Graph a normal probability plot of the data.
4. Comment on the data.

Question 2:

The April 22, 1991 issue of Aviation Week and Space Technology reports that during Operation Desert Storm, U.S. Airforce F-117A pilots flew 1270 combat sorties for a total of 6905 hours. What is the mean duration of an F-117A mission during this operation? Why is the parameter you have calculated a population mean?

14.- A sociologist asserts that only 5% of all seniors in high school, capable of performing work at the university level, actually attend university. Find the probabilities that among 180 students capable of performing work at university level:
a) exactly 10 attend college using the binomial
b) Using the normal distribution
c) at least 10 go to university using binomial T.I or excel
d) Using the normal distribution
e) when many eight go to university using binomial or excel
f) Using the normal distribution

The mean of a population is 77 and the standard deviation is 12. The shape of the population is unknown. Determine the probability of each of the following occurring from this population. a. A random sample of size 35 yielding a sample mean of 81 or more

b. A random sample of size 150 yielding a sample mean of between 76 and 80

c. A random sample of size 221 yielding a sample mean of less than 77.2

(Round all the values of z to 2 decimal places and final answers to 4 decimal places.)