Can the cost of flying a commercial airliner be predicted using regression analysis? If so, what variables are related to this cost? A few of many variables that can potentially contribute are type of plane, distance, number of passengers, amount of luggage/freight, weather condition, direction of destination, or even pilot skill. Suppose a study is conducted using only Boeing 737s traveling 800 km on comparable routes during the same season of the year. Can the number of passengers predict the cost of flying such routes? It seems logical that more passengers result in more mass and more baggage, which could, in turn, result in increased fuel consumption and other costs. Suppose the data displayed below are the cost and associated number of passengers for thirty-six 800-km commercial airline flights using Boeing 737s during the same season of the year. We will use these data to develop a regression model to predict cost by number of passengers.

The data contains the data on the cost and number of passengers of 36 observations.

(f) Using an αα of 5%, this data indicates that  ? Cost of flying a commercial flight using Boeing 737s the number of passengers   ? can cannot  be expressed as a linear function of  ? Cost of flying a commercial flight using Boeing 737s the number of passengers .

(g) Find a 95% confidence interval for the slope term of the model, β1β1.

Lower Bound =

(use three decimals in your answer)

Upper Bound =

(use three decimals in your answer)

(i) With 95% confidence, find the average cost of flying a commercial flight using Boeing 737s when the number of passengers is 70.

Lower Bound =

(use three decimals in your answer)

Upper Bound =

(use three decimals in your answer)

Many food products contain small quantities of substances that would give an undesireable taste or smell if they are present in large amounts. An example is the "off-odors" caused by sulfur compounds in wine. Oenologists (wine experts) have determined the odor threshold, the lowest concentration of a compound that the human nose can detect. For example, the odor threshold for dimethyl sulfide (DMS) is given in the oenology literature as 25 micrograms per liter of wine (µg/l). Untrained noses may be less sensitive, however. Here are the DMS odor thresholds for 10 beginning students of oenology.

41 32 24 35 33 26 36 22 30 31

Assume (this is not realistic) that the standard deviation of the odor threshold for untrained noses is known to be σ = 7 µg/l.

(a) Make a stemplot to verify that the distribution is roughly symmetric with no outliers. (A normal quantile plot confirms that there are no systematic departures from normality. Enter numbers from smallest to largest, separated by spaces. Enter NONE for stems with no values.)

2

2

3

3

4

(b) Give a 95% confidence interval for the mean DMS odor threshold among all beginning oenology students. (Round your answers to three decimal places.) ,

(c) Are you convinced that the mean odor threshold for beginning students is higher than the published threshold, 25 µg/l? Carry out a significance test to justify your answer. (Use α = 0.05. Round your value for z to two decimal places and round your P-value to four decimal places.) z = P-value =

State your conclusion.

Reject the null hypothesis. There is significant evidence that the mean odor threshold for beginning students is higher than the published threshold.

Reject the null hypothesis. There is not significant evidence that the mean odor threshold for beginning students is higher than the published threshold.

Fail to reject the null hypothesis. There is significant evidence that the mean odor threshold for beginning students is higher than the published threshold.

Fail to reject the null hypothesis. There is not significant evidence that the mean odor threshold for beginning students is higher than the published threshold.

The Capital Asset Price Model (CAPM) is a financial model that attempts to predict the rate of return on a financial instrument, such as a common stock, in such a way that it is linearly related to the rate of return on the overal market. Specifically,

RStockA,i = β0 + β1RMarket,i + ei

You are to study the relationship between the two variables and estimate the above model:

iRStockA,i - rate of return on Stock A for month i, i=1,2,⋯59.

iRMarket,i - market rate of return for month ii, i=1,2,⋯,59

β1 represent's the stocks 'beta' value, or its systematic risk. It measure's the stocks volatility related to the market volatility. β0 represents the risk-free interest rate.

The data in the  file contains the data on the rate of return of a large energy company which will be referred to as Acme Oil and Gas and the corresponding rate of return on the Toronto Composite Index (TSE) for 59 randomly selected months.

Therefore RAcme,i represents the monthly rate of return for a common share of Acme Oil and Gas stock; RTSE,i represents the monthly rate of return (increase or decrease) of the TSE Index for the same month, month ii. The first column in this data file contains the monthly rate of return on Acme Oil and gas stock; the second column contains the monthly rate of return on the TSE index for the same month.

(e, ii) Use the FF-test, test the statistical hypotheses determined in (e, i). Find the value of the test statistic, using three decimals in your answer.

Fcalc =

(e, iii) Find the P-value of your result in (e, ii). Use three decimals in your answer.

P-value =

(f) Find a 95% confidence interval for the slope term of the model, β1.

Lower Bound =

(use three decimals in your answer)

Upper Bound =

(use three decimals in your answer)


(h) Find a 95% confidence interval for the β0 term of the model.

Lower Bound =

(use three decimals in your answer)

Upper Bound =

(use three decimals in your answer)


(k) Last month, the TSE Index's monthly rate of return was 1.5%. This is, at the end of last month the value of the TSE Index was 1.5% higher than at the beginning of last month. With 95% confidence, find the last month's rate of return on Acme Oil and Gas stock.

Lower Bound =

(use three decimals in your answer)

Upper Bound =

(use three decimals in your answer)

Bob Sparrow purchases steak from a local meatpacking house. The meat is purchased on Monday at $2.00 per pound, and the shop sells the steak for $3.00 per pound. Any steak left over at the end of the week is sold to a local zoo for $0.50 per pound. The possible demands for steak and the probability of each are shown in the following table:

Demand (lbs.) Probability

20 0.2

21 0.3

22 0.5

Bob must decide how much steak to order in a week. Bob wants to maximize expected value. What is his expected value when purchasing optimally? [Hint: construct a payoff table for each of his decisions and each state of nature.] A) 20 B) 20.5 C) 20.25 D) 21 9.

What is Bob Sparrow’s Expected Value of Perfect Information? A) 20.5 B) 1.3 C) 0.8 D) 1.05

2. Using the SCC men’s/women’s class sample data at the ?=0.05, is there enough evidence to conclude that there is a significant linear correlation between men’s/women’s height and men’s/women’s shoe size?

a. State the null and alternate hypotheses.

b. Specify the level of significance.

c. State the correlation coefficient. (3 decimal places)

d. State the critical value from Table 11. (Use the value of n that is closest to your sample size.)

e. State whether to “reject the ?0” or “fail to reject the ?0”.

f. Interpret the decision in the context of the original claim

6. The heights of women are normally distributed with a mean of 65 in. and a standard deviation of 2.5 in. The heights of men are normally distributed with a mean of 70 in. and a standard deviation of 3.0 in. Relative to their peers, who would be considered taller: A 68 in. woman or a 74 in. man?

7. The lengths of adult blue whales are normally distributed with a mean of 30 meters and a standard deviation of 6 meters. What is the probability that a randomly selected adult blue whale would have a length that differs from the population mean by less than 3 meters?

Thank you for answering!!!

A pharmaceutical company is evaluating its efficiency of its glucose control drug. The company believes that the drug controls glucose levels with the normal range of 80 to 115. A sample of 100 customers were found to have a mean of level of 102 with a standard deviation 12, can we conclude that the mean for this population is greater than 80 and less than 115, the sample is 100 and alpha is 0.5

Stata command for running an RDD with 2 treamtents and cut-off lines

According to a 2004 report by Roger Boe et. Al. of Correctional Service Canada, the mean length of a Canadian jail sentence in 2001/2002 was ? = 4.10 months with σ = 9.75 months.

a) Can we assume that prison sentences are normally distributed? Please explain.

b) Using the central limit theorem, what is the approximate probability that the mean sentence for a random sample of 225 prisoners is more than 4.75 months?

1. From a sample of 64 days, General Motors register a X of 3.58 accidents pe day with s = of 52. What is confidence interval covers that the mean number of accidents per day at the factory is between 3.2 and 3.96 accidents?

1. Construct and interpret a correlation matrix for your data. and explain the relationship.
2. Show the step wise process of determining the best regression model to predict PRICE. EXPLAIN the process as you move from the full model to your final model.
3. make 3 regression models based on cars, bedroom, bath room.
4. Using your final model, select values for the independent variables and predict the house’s sales price.

Calculate the test statistic and p-value for each sample mean and make the statistical decision (3 points each).

1. H0: µ ≤ 16 versus H1: µ > 16, x = 17, s = 5, n = 25, α = 0.05 test statistic___________ p-value___________ Decision (circle one) Reject the H0 Fail to reject the H0

2. H0: µ ≥ 205 versus H1: µ < 205, x = 198, σ = 15, n = 20, α = 0.05 test statistic___________ p-value___________ Decision (circle one) Reject the H0 Fail to reject the H0

3. H0: µ = 26 versus H1: µ<> 26, x = 22, s = 10, n = 30, α = 0.01 test statistic___________ p-value___________ Decision (circle one) Reject the H0 Fail to reject the H0

4. H0: µ ≥ 155 versus H1: µ < 155, x = 145, σ = 19, n = 25, α = 0.01 test statistic___________ p-value___________ Decision (circle one) Reject the H0 Fail to reject the H0

5. H0: µ ≥ 155 versus H1: µ < 155, x = 145, σ = 19, n = 15, α = 0.01 test statistic___________ p-value___________ Decision (circle one) Reject the H0 Fail to reject the H0

6. The mean cost of a basic rental car per week is said to be greater than $125 per week. To determine if this is true, a random sample of 25 rental cars is taken and resulted in an average of $130.50 and an sample standard deviation of $15.40. Test the appropriate hypotheses at  = 0.05 (1 point each). H0: _________________ H1: _________________ Test statistic : _________________ p-value : _________________ Is the mean cost greater than $125/week ? (circle one) YES NO

Find the mean and variance of the gamma distribution using integration to obtain E(X) and E(X^2 ).

[Hint: Express the integrand in terms of a gamma density.]

[Hint: Use the fact that the integral of a valid pdf must be equal to 1.]

1. Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

A safety administration conducted crash tests of child booster seats for cars. Listed below are results from those​ tests, with the measurements given in hic​ (standard head injury condition​ units). The safety requirement is that the hic measurement should be less than 1000 hic. Use a 0.05 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. Do the results suggest that all of the child booster seats meet the specified​ requirement?

751, 801, 1230, 657, 630, 557

a. identify the test statistics( round to 3 decimal places)

b. The P- value ? (round to 4 decimal places)

c what do the results suggest about the child booster seats meeting the specified requirement

3.  Listed below are the lead concentrations in μ​g/g measured in different traditional medicines. Use a 0.05 significance level to test the claim that the mean lead concentration for all such medicines is less than 17 μ​g/g. Assume that the lead concentrations in traditional medicines are normally distributed.

8, 21.5 , 19, 10.5 , 11.5 , 8.5 , 6, 15, 7.5 , 19

a. determine the test statistics

b. determine the P-value

4. A group of students estimated the length of one minute without reference to a watch or​ clock, and the times​ (seconds) are listed below. Use a 0.10 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one​ minute?

66, 80, 42, 66, 45, 27, 57, 63, 66, 49, 64, 69, 93, 89, 64

a. determine the test statistics

b. determine the p-value

In a study of the role of young drivers in automobile accidents, data on the percentage of licensed drivers under the age of 21 and the number of fatal accidents per 1000 licenses were determined for 32 cities. The first column contains a number as city code, the second column contains the percentage of drivers who are under 21, and the third column contains the number of fatal accidents is dependent upon the proportion of licensed drivers that are under 21.

Use 30 degrees of freedom, and alpha as 0.01 to get a critical value of 1.697)

16. What is the margin of error for calculating a 90% interval for the slope of the true regression line? (i.e. 1.697 by the standard deviation of the slope

17. What is the lower 90% confidence limit for the slope?

18. What is the upper 90% confidence limit of the slope?

19. What is the value of the test statistic for testing this hypothesis?