# Project #38349 - STATISTICS

STAT 690

Summer 2014

Question 1

.    If you increase the confidence level, the confidence interval

A. decreases

B. increases

C. stays the same

D. may decrease or increase

2.)

.    In developing an internal estimate for a population mean, the population standard deviation, sigma, was assumed to be 10. The interval estimate was 50.92 +- 2.14. Had sigma equaled 20, the interval estimate would be:

 . .    a. .    60.92 +- 2.14 . .    b. .    50.92+ -12.14 . .    c. .    101.84+ -4.28 .    d. .    50.92 +- 4.28

3.) Suppose that a confidence interval for the population mean is between 62.84 and 69.46. The population standard deviation is assumed to be 6.50 and the sample size is 100. The sample mean is ….

a.

6.21

b.

66.21

c.

66.15

d.

6.62

4.) You are interested in determining the average cost of a 3-minute telephone call to locations within the continental U.S. What sample size must you take to be 96% confident that the results will be within 0.75 of the true mean cost per call given that the standard deviation of the population, sigma is equal to 7.71?

a.)  573

b.) 446

c.) 406

d. )574

5.) If the coefficient of determination is 0.975, then the slope of the regression line …

 a. is negative b. is positive c. could be either positive or negative d. is a straight line

6.) A slope estimate of zero in a linear regression output indicates:

 a. a strong linear relationship b. a weak linear relationship c. no linear relationship d. a perfect linear relationship

7.) If we don’t make the assumption of additivity in a multiple regression model with independent variables GENDER and SENIORITY and dependent variable INCOME, the interpretation of the interaction slope coefficient (b3) would be:

 a. ) b3 is the change in SENIORITY when we go from GENDER = female to GENDER = male b.) b3 is the mean value of INCOME when the two independent variables are 0 c. ) b3 is the change in the relationship between SENIORITY and INCOME between different values of GENDER d. ) none of the above

8.) We are interested in determining a 90% confidence interval for the proportion of US citizens who exercise more than one hour per week. The sample proportion we find based on a sample of more than 1000 people is 0.34. The confidence interval could only be one of the following:

 a. [0.21, 0.36] b. [0.20, 0.30] c. [0.30, 0.40] d. [0.28, 0.40]

9.) You take a sample of size 50 from a population with known mean of 500 and known standard deviation of 120. Which of the following would be a result predicted by the Central Limit Theorem:

 a. the sampling distribution of sample means is approximately normal b. the standard deviation of the sampling distribution of sample means is about 16.97 c. the mean of the sampling distribution of the sample means is 0 d. a and b e. a and c

10.) In linear regression, the fitted value is the:

 a. Predicted value of the dependent variable b. Predicted value of the slope c. Predicted value of the independent variable d. Predicted value of the intercept

11.) The file Auction.xlsx (that has been sent to you through email) contains the information of 1000 auctions on eBay.com. The data include variables that describe what seller selected (auction duration, day-of-week auction closes (weekday/weekend), opening price). In addition, we have the price at which the auction closed and whether the auction was a ‘competitive auction’. A competitive auction is defined as an auction with at least two bids placed on the item auctioned. The two variables that should be treated as discrete variables are ‘endDay’ and ‘Competitive?’. As an analyst, you have been asked to compare the closing price on weekdays to weekends to see whether they are any different. (Please type your answers in the provided space. Make sure to separate your answers to each part by typing the part/section number (a,b,c,…)).

a. Does this analysis involve paired samples or independent samples? Explain Why.

b. State your alternative hypothesis in words.

c. Which table in the output contains the output of interest? Explain why.

d. Report the degrees of freedom.

e. Report the calculated test statistic.

f. Report the calculated p-value.

12.) Refer to the Auction dataset: Based on historical data, it’s hypothesized that the number of competitive auctions are 1.5 times more than number of non-competitive auctions. In analyzing this hypothesis, please answer the following questions:

a. State your alternative hypothesis in words.

b. What statistical test you would use to test this hypothesis?

c. Test the hypotheses at the 0.1 significance level, report the critical value (rejection region), the calculated test statistic and its associated p-value.

13.) Refer to the Auction dataset: In an attempt to predict the closing price, you’re testing the significance of the following set of predictors: ‘Duration’, ‘OpenPrice’ and ‘endDay’ (with ‘weekend’ being its category of interest). Please run a multiple regression with all of these independent variables. Then report the following numbers and answer the following questions.

a. Report the R-squared.

b. Is your model significant? Explain why or why not.

c. Report the estimated coefficient of ‘OpenPrice’. What is your interpretation of this number?

d. Report the estimated coefficient of ‘endDay’. What is your interpretation of this number?

e. We’re interested to see whether Duration has a positive effect on the closing price. Does that data support this hypothesis? Explain why or why not. In doing so, report the relevant test statistics and p-value.

 Subject Mathematics Due By (Pacific Time) 08/22/2014 08:00 pm
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