Question 15

Please answer the following set of questions, based on the information provided below.

A service company is curious to know whether customer age is crucial in deciding to subscribe. The company has collected a random sample of 1000 people, and asked everyone whether he or she would subscribe to the service. The company knows which age group the person falls into: under 18 years of age, 18 - 29 years of age, 30-45 years of age and 46 years or older. The company decides to use a chi-square test of independence at 0.05 level of significance to answer its questions. Below are the sample’s data:

What is the expected value for the second age group [18-29] choosing NOT to subscribe?

Question 14

Please answer the following set of questions, based on the information provided below.

A service company is curious to know whether customer age is crucial in deciding to subscribe. The company has collected a random sample of 1000 people, and asked everyone whether he or she would subscribe to the service. The company knows which age group the person falls into: under 18 years of age, 18 - 29 years of age, 30-45 years of age and 46 years or older. The company decides to use a chi-square test of independence at 0.05 level of significance to answer its questions. Below are the sample’s data:

What is the degrees of freedom (df) for this test?

A box contains three 40 Watt bulbs, eight 60 Watt bulbs, and nine 100 Watt bulbs. If you drew a sample of three bulbs without replacement what is the probability within that sample that there are more 60 Watt bulbs than 40 Watt bulbs?

Following is the payoff table for the Pittsburgh Development Corporation (PDC) Condominium Project. Amounts are in millions of dollars.

Suppose PDC is optimistic about the potential for the luxury high-rise condominium complex and that this optimism leads to an initial subjective probability assessment of 0.8 that demand will be strong (S₁) and a corresponding probability of 0.2 that demand will be weak (S₂). Assume the decision alternative to build the large condominium complex was found to be optimal using the expected value approach. Also, a sensitivity analysis was conducted for the payoffs associated with this decision alternative. It was found that the large complex remained optimal as long as the payoff for the strong demand was greater than or equal to $17 million and as long as the payoff for the weak demand was greater than or equal to -$20 million.

A) Consider the medium complex decision. How much could the payoff under strong demand increase and still keep decision alternative d₃ the optimal solution? If required, round your answer to two decimal places.The payoff for the medium complex under strong demand remains less than or equal to $ ________ million, the large complex remains the best decision.

B) Consider the small complex decision. How much could the payoff under strong demand increase and still keep decision alternative d₃ the optimal solution? If required, round your answer to two decimal places. The payoff for the small complex under strong demand remains less than or equal to $________ million, the large complex remains the best decision.

Let X1, X2, . . . be a sequence of independent and identically distributed random variables where the distribution is given by the so-called zero-truncated Poisson distribution with probability mass function; P(X = x) = λ^x/ (x!(eλ − 1)), x = 1, 2, 3...

Let N ∼ Binomial(n, 1−e^−λ ) be another random variable that is independent of the Xi ’s.

1) Show that Y = X1 +X₂ + ... + X_N has a Poisson distribution with mean nλ.

The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains.† Assume the following data are representative of the results reported. The variable type indicates whether the restaurant is an Italian restaurant or a seafood/steakhouse. Price indicates the average amount paid per person for dinner and drinks, minus the tip. Score reflects diners' overall satisfaction, with higher values indicating greater overall satisfaction. A score of 80 can be interpreted as very satisfied. (Let x₁ represent average meal price, x₂ represent type of restaurant, and y represent overall customer satisfaction.)

(a)

Develop the estimated regression equation to show how overall customer satisfaction is related to the independent variable average meal price. (Round your numerical values to two decimal places.)

ŷ = ___________

(b)

At the 0.05 level of significance, test whether the estimated regression equation developed in part (a) indicates a significant relationship between overall customer satisfaction and average meal price. (Use an F test.)

Find the value of the test statistic. (Round your answer to two decimal places.) __________

Find the p-value. (Round your answer to three decimal places.)

p-value = 0.005

(d)

Develop the estimated regression equation to show how overall customer satisfaction is related to the average meal price and the type of restaurant. (Use the dummy variable developed in part (c). Round your numerical values to two decimal places.)

ŷ = __________

Find the value of the test statistic. (Round your answer to two decimal places.) __________9.99 and 10.00 are both wrong

Find the p-value. (Round your answer to three decimal places.)

p-value = ____________0.001 and 0.00 are both wrong

Predict the Consumer Reports customer satisfaction score for a seafood/steakhouse that has an average meal price of $15. (Round your answer to two decimal places.)  

How much would the predicted score have changed for an Italian restaurant? (Round your answer to two decimal places.) 75.95

The predicted satisfaction score increases by __________ points for Italian restaurants

Research performed at NASA and led by Dr. Emily R. Morey-Holton measured the lengths of the right humerus and right tibia in 11 rats that were sent into space on Spacelab Life Sciences 2. The following data were collected:

a) Treating the length of the right humerus as the explanatory variable, x, determine the estimates of beta0 and beta1

b) Compute the standard error of the estimate

c) Determine whether the residuals are normally distributed

d) If the residuals are normally distributed, determine sb1

e) If the residuals are normally distributed, test whether a linear relation exists between the length of the right humerus, x, and the length of the right tibia, y, at the alpha=0.01 level of significance

f) If the residuals are normally distributed, construct a 99% confidence interval for the slope of the true least-squares regression line.

g) What is the mean length of the right tibia on a rat whose right humerus is 25.93 mm?

Forecast the advertising revenue for each quarter in 2011 using seasonal dummy variables and a best subsets regression.​ (Let the first dummy variable be equal to 1 for Quarter 2 and so​ on, following the order of the seasonal categories in the given​ table.

2008

2009

2010

A) The revenue forecast for the first quarter in 2011 is?

The revenue forecast for the second quarter in 2011 is?

The revenue forecast for the third quarter in 2011 is?

The revenue forecast for the fourth quarter is?

B.) quarter 4 has an average revenue that is ___ above that for quarter !

C.) Calculate the MAD for the forecast.

It is known that 1 year old dogs have a mean gain in weight of 1.0 pound per month with a standard deviation of 0.40 pound. A special diet supplement, Helthpup, is given to a rando sample of 36, 1-year-old dogs for a month; their mean gain in weight is 2.15 pounds. At the 0.01 level of significance, does helthpup affect weight gain in 1-year-old dogs? (a) What is the research problem? (b) State null and alternative hypothesis (c) Is this one or two tail test? why? (d) what is the critical value? (e) what is the decision rule? (f) calculate the statistic (g) what is your decision regarding null hypothesis and why? (h)interpretation of the results?

A bottled water distributor wants to estimate the amount of water contained in 11​-gallon bottles purchased from a nationally known water bottling company. The water bottling​ company's specifications state that the standard deviation of the amount of water is equal to 0.04 gallon. A random sample of 50 bottles is​ selected, and the sample mean amount of water per 11​-gallon bottle is 0.983 gallon. Complete parts​ (a) through​ (d).

A. Construct a 95% confidence interval estimate for the population mean amount of water included in a 1-gallon bottle

___ ≤ μ ≤ ____

b. On the basis of these​ results, do you think that the distributor has a right to complain to the water bottling​company? Why?

c. Must you assume that the population amount of water per bottle is normally distributed​ here? Explain.

D. Construct a 90​% confidence interval estimate. How does this change your answer to part​ (b)?

In R code please: Test the hypothesis whether the students smoking habit (Smoke) is independent of their exercise level (Exer) in dataset survey (MASS package) at 0.05 significance level.

(Please include how to download the MASS package. Thanks.)

Modern medical practice tells us not to encourage babies to become too fat. Is there a positive correlation between the weight, x, or a 1-year-old baby and the weight, y, of the mature adult (30 years old)? A random sample of medical files produced the following information for 14 females. Please use this data to answer all parts of the question.

x (lbs) 21 25 23 24 20 15 25 21 17 24 26 22 18 19

y (lbs) 125 125 120 125 130 120 145 130 130 130 130 140 110 115

note: For these data, ?̅≈ 21.42, ?? ≈ 3.32, ?̅ ≈ 126.79, ?? ≈ 9.12 1.

Use a 5% level of significance to test the claim that ? > 0.

a. State the null and alternative hypotheses.

?0:

?1:

b. What calculator test will you use? List the requirements that must be met for you to use this test, and indicate whether the conditions are met in this problem.

c. Run the calculator test and obtain the P-value.

d. Based on your P-value, will you reject or fail to reject the null hypothesis?

e. Interpret your conclusion from part d in the context of this problem. In other words, what does this result tell you about the population correlation between the weight of a child at 1 year, and their corresponding weight as an adult?

Explain what an influential multivariate outlier is, and at least two methods of coping with them in multiple regression.