An individual buys 10 raffle tickets in hopes of winning one of 15 prizes to be given away by drawing tickets without replacement. The total number of raffle tickets sold is 168. Lt X be the number of prizes won by the individual.

A) Find the probability the individual wins at least one prize

B) Calculate the expected value E(X) accurate to 4 decimal places

C) Calculate the standard deviation SD(X) accurate to 4 decimal places

DATE FILE MPG2

Use Data Set G, Mileage and Vehicle Weight, on page 536 of your textbook to answer the following questions. The data are found in the Excel Data file, MPG2, which is posted on Canvas under Modules under Chapter 12 Textbook data. The first column (Weight) is X, or the independent, variable and the second column (City MPG) is Y, or the dependent, variable. Use MINITAB to obtain the simple regression equation, confidence interval, prediction interval, and required graphs. Insert tables and graphs in your report as appropriate.

Use Minitab and produce the appropriate output to answer the following questions. Attach the output.

1. Construct a scatter plot. Recalling what scatter plots are used for, write a couple of sentences addressing what you observed from the plot. Be sure to relate your observations to the purpose of using scatter plots in regression. (4 points)

2. Can we conclude that Weight of a vehicle helps in predicting City MPG? Follow the 7 steps for hypothesis testing. (12 points)

3. Find the sample regression equation and interpret the coefficients. Remember your interpretations should be in terms of the problem. (4 points)

4. Find the coefficient of determination, and interpret its value. (2 points)

5. Use residual analysis to check the validity of the model and fully explain your findings and conclusions. (6 points)

6. Estimate with 95% confidence the average City MPG all vehicles with a Weight of 3500 lbs. Predict with 95% confidence the City MPG for an individual vehicle with a weight of 3500 lbs. Write at least one sentence using your confidence interval and at least one sentence using your prediction interval. (10 points)

7. Verify that the p-value for the F is the same as the slope t statistic’s p-value, and show that t2 = F. (2 points)

Which type of t inference procedure?

(A: one sample, B: matched pairs, C: two samples)

1. ______Is blood pressure altered by use of an oral contraceptive? Comparing a sample of women not using an OC with a sample of women taking it.

2. ______Average cholesterol level in general adult population is 175 mg/dl. Take a sample of adults with ‘high cholesterol’ parents. Is the mean cholesterol level higher in this population?

3. ______Does bread lose vitamin with storage? Take a sample of bread loaves and compare vitamin content right after baking and again after 3 days later.

4. ______Does bread lose vitamin with storage? Take a sample of bread loaves just baked and a sample of bread loaves stored for 3 days and compare vitamin content.

Nowadays, movies can be rented from a vending machine located at the entrance to many stores.  Suppose that it is now Friday evening at 8pm and a certain machine within a certain store has six copiesof the movie “Twilight” available for rent.  The machine will not be visited by the owner until Sunday afternoon at noon (which is 40hrs later), at which time returned movies will be restocked.

Suppose that customers wanting to rent “Twilight” arrive at this rental machine at a rate of 1 every 5 hours.

LetW= the time (in hours) until the next “Twilight” renter arrives at the machine.

Name the distribution of Wand identify the parameter.

Distribution name:  ___________________

Parameter value:  ___________________

What is the chance the next “Twilight” renter arrives sometime on Saturday?

      Thus, we seek the P( ___ < W< ___ ) which equals ________________?

LetX= the number of renters wanting “Twilight” that come to the

vending machine over the weekend (Fri 8pm until Sunday noon).

Name the distribution of Xand identify the parameter.

Distribution name:  ___________________

Parameter value:  ___________________

What is the probability that exactly 4 copies of “Twilight” are rented over

       the weekend?  Thus, we seek the P(X= 4) which equals ________________?

What is the probability that all copies of “Twilight” are rented over the

      weekend?  Thus, we seek  P( X __  __ ) which equals ________________?

A psychologist wants to determine if aging has an impact on depression. It is known that the general population scores a 41 on a standardized depression test where a higher score indicates more depression. The psychologist obtains a sample of individuals that are all over 67 years old. What can the psychologist conclude with an α of 0.01? The data are below.

a) What is the appropriate test statistic?
---Select--- na z-test One-Sample t-test Independent-Samples t-test Related-Samples t-test

b)
Population:
---Select--- aging standardized depression test depression elderly general population
Sample:
---Select--- aging standardized depression test depression elderly general population

c) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0

d) Using the SPSS results, compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d =  ;   ---Select--- na trivial effect small effect medium effect large effect
r² =  ;   ---Select--- na trivial effect small effect medium effect large effect

e) Make an interpretation based on the results.

The elderly are significantly more depressed than the population.

The elderly are significantly less depressed than the population.    

The elderly did not significantly differ on depression than the population

1. Suppose that a fire insurance company wants to relate the amount of fire damage in major residential fires to the distance between the burning house and the nearest fire station. The study is to be conducted in a large suburb of a major city. A sample of 14 recent fires in this suburb is selected. The amount of damage, y, and the distance between the fire and the nearest station, x, are given below. We are interested in building a regression model to predict fire damage y, given the distance from the fire x.

1. Is the predictor distance significant? What is the test statistic and p value?
2. What is the amount of variation explained in the model?
3. What is the standard error of the estimated regression line?
4. Use the final regression equation to predict the damage caused by the fire that is 6.5 miles away from the nearest station.

A charity organization hosts a raffle drawing at a fund raising event. The organization sells 2500 tickets at a price of $8 each. Winning tickets are randomly selected, with 30 prizes of $100, 10 prizes of $500, and 1 grand prize of $8000. Suppose you buy one ticket. Let the random variable X represent your net gain from playing the game once (remember that the net gain should include the cost of the ticket). Use the table below to help you construct a probability distribution for all of the possible values of X and their probabilities. Find the mean/expected value of X. (Round to two decimal places.) In complete sentences, describe the interpretation of what your value from #2 represents in the context of the raffle. If you were to play in such a raffle 100 times, what is the expected net gain? Would you choose to buy a ticket for the raffle? (Your response should be a short paragraph, written in complete sentences, to explain why or why not.) What ticket price would make it a fair game, so that, on average, neither the players nor the organizers of the raffle win or lose money? (Round to two decimal places.)

4. In a normal distribution with ?(?) = 100 and ??(?) = 16, find the predicted a. 8th percentile. b. 22nd percentile. c. median. d. ?3. e. 95th percentile.

6 In a data set, ? = 38, ?̅= 110.4, and ? = 20.9. In a normal distribution having the same features, find a. the predicted 30th percentile. b. the predicted 70th percentile. c. the predicted percentile corresponding to the 20th ordered data value. d. the predicted percentile corresponding to the 6th ordered data value.

Use Minitab to construct an 85% confidence interval for the proportion of all residents in the state that favor a pro-nuclear energy policy. Please show me the steps.

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Given trap spacings among two lobster fishing crews: BT cooperative has spacings = {93, 99, 105, 94, 82, 70, 86} PA cooperative has spacings = {118, 94, 106, 72, 90, 66, 153, 98}

a) Set up null and alternative hypotheses for testing the equality of variances

b) Find the sample variances for the two cooperatives.

c) Compute the test statistic.

d) Find the approximate p-value of the test.

e) Make a conclusion if ? = .01.

1. Given PMF f(x) =(x^2−3)/20 for X= 2,3,4

•Make a probability distribution table for X

•Find the CDF of X,F(x)

•Find the mean of X,μX, and the S.D. of X,σX

•If Y=1/3 X+ 2, find the mean of Y,μY, and the S.D. of YσY

Sample statistics for a local bank and a competitor's bank

1. Are the samples dependent or independent?
2. State your Null/Alternative hypotheses
3. What is the test-statistic?
4. What is the p-value?
5. What are the critical values?
6. Does the test-statistic lie in the rejection region?
7. Interpret the Result?
8. Does the result change for a different value of alpha? Explain?

13))

A sample containing years to maturity and yield for 40 corporate bonds are contained in the data given below.

a. What is the sample mean years to maturity for corporate bonds and what is the sample standard deviation?

Mean (to 4 decimals) _____ Standard deviation______ (to 4 decimals)

b. Develop a 95% confidence interval for the population mean years to maturity. Round the answer to four decimal places. ( , )years

c. What is the sample mean yield on corporate bonds and what is the sample standard deviation?

Mean _________(to 4 decimals) Standard deviation __________(to 4 decimals)

A political scientist hypothesize that a political ad will increase attitudes about a particular issue. The scientist randomly asks 25 individuals walking by to see the ad and then take a quiz on the issue. The general public that knows little to nothing about the issue, on average, scores 50 on the quiz. The individuals that saw the ad scored an average of 47.55 with a variance of 28.73. What can the political scientist conclude with an α of 0.05?

a) What is the appropriate test statistic?
---Select--- na z-test one-sample t-test independent-samples t-test related-samples t-test

b)
Population:
---Select--- the ad individuals walking by general public the particular issue the political ad
Sample:
---Select--- the ad individuals walking by general public the particular issue the political ad

c) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[  ,  ]

e) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d =  ;   ---Select--- na trivial effect small effect medium effect large effect
r² =  ;   ---Select--- na trivial effect small effect medium effect large effect

f) Make an interpretation based on the results.

Individuals that watched the political ad scored significantly higher on the quiz than the general public.Individuals that watched the political ad scored significantly lower on the quiz than the general public.    Individuals that watched the political ad did not score significantly different on the quiz than the general public.