21. Ages of Robbery Victims A recent study in a small city stated that the average age of robbery victims was 63.5 years. A sample of 20 recent victims had a mean of 63.7 years and a standard deviation of 1.9 years. At a 0.05, is the average age higher than originally believed? Use the P-value method.

21. Ages of Robbery Victims A recent study in a small city stated that the average age of robbery victims was 63.5 years. A sample of 20 recent victims had a mean of 63.7 years and a standard deviation of 1.9 years. At a 0.05, is the average age higher than originally believed? Use the P-value method.

Essentials of Business Analytics (MindTap Course List)

2nd Edition

ISBN:9781305627734

Author:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson

Publisher:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson

Chapter6: Statistical Inference

Section: Chapter Questions

Problem 16P

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Say that an analyst has looked at a random sample of 50 companies in the S&P 500 to understand the association between a stock's P/E ratio and subsequent 12-month performance in the market. Assume that the resulting estimate is -0.20, indicating that for every 1.0 point in the P/E ratio, stocks return 0.2% poorer relative performance. In the sample of 52, the standard deviation was found to be 2.7. What is the standard of error?
Consider again the example introduced in Section 7.5 of a credit card company that has a database of information provided by its customers when they apply for credit cards. An analyst has created a multiple regression model for which the dependent variable in the model is credit card charges accrued by a customer in the data set over the past year (y), and the independent variables are the customers annual household income (x1), number of members of the household (x2), and number of years of post-high school education (x3). Figure 7.23 provides Excel output for a multiple regression model estimated using a data set the company created. a. Estimate the corresponding simple linear regression with the customers annual household income as the independent variable and credit card charges accrued by a customer over the past year as the dependent variable. Interpret the estimated relationship between the customers annual household income and credit card charges accrued over the past year. How much variation in credit card charges accrued by a customer over the past year is explained by this simple linear regression model? b. Estimate the corresponding simple linear regression with the number of members in the customers household as the independent variable and credit card charges accrued by a customer over the past year as the dependent variable. Interpret the estimated relationship between the number of members in the customers household and credit card charges accrued over the past year. How much variation in credit card charges accrued by a customer over the past year is explained by this simple linear regression model? c. Estimate the corresponding simple linear regression with the customers number of years of posthigh school education as the independent variable and credit card charges accrued by a customer over the past year as the dependent variable. Interpret the estimated relationship between the customers number of years of posthigh school education and credit card charges accrued over the past year. How much variation in credit card charges accrued by a customer over the past year is explained by this simple linear regression model? d. Recall the multiple regression in Figure 7.23 with credit card charges accrued by a customer over the past year as the dependent variable and customers annual household income (x1), number of members of the household (x2), and number of years of post-high school education (x3) as the independent variables. Do the estimated slopes differ substantially from the corresponding slopes that were estimated using simple linear regression in parts (a), (b), and (c)? What does this tell you about multicollinearity in the multiple regression model in Figure 7.23? e. Add the coefficients of determination for the simple linear regression in parts (a), (b), and (c), and compare the result to the coefficient of determination for the multiple regression model in Figure 7.23. What does this tell you about multicollinearity in the multiple regression model in Figure 7.23? f. Add age, a dummy variable for sex, and a dummy variable for whether a customer has exceeded his or her credit limit in the past 12 months as independent variables to the multiple regression model in Figure 7.23. Code the dummy variable for sex as 1 if the customer is female and 0 if male, and code the dummy variable for whether a customer has exceeded his or her credit limit in the past 12 months as 1 if the customer has exceeded his or her credit limit in the past 12 months and 0 otherwise. Do these variables substantially improve the fit of your model?
Please calculate the Sharpe measure for the S&P 500 over the last ten years if the standard deviation was 8 percent and the return was 14 percent?
Consider again the example introduced in Section 4.5 of a credit card company that has a database of information provided by its customers when the customers apply for credit cards. An analyst has created a multiple regression model for which the dependent variable in the model is credit card charges accrued by a customer in the data set over the past year (y), and the independent variables are the customers annual household income (x1), number of members of the household (x2), and number of years of posthigh school education (x3). Figure 4.23 provides Excel output for a multiple regression model estimated using a data set the company created. a. Estimate the corresponding simple linear regression with the customers annual household income as the independent variable and credit card charges accrued by a customer over the past year as the dependent variable. Interpret the estimated relationship between the customers annual household income and credit card charges accrued over the past year. How much variation in credit card charges accrued by a customer over the past year does this simple linear regression model explain? b. Estimate the corresponding simple linear regression with the number of members in the customers household as the independent variable and credit card charges accrued by a customer over the past year as the dependent variable. Interpret the estimated relationship between the number of members in the customers household and credit card charges accrued over the past year. How much variation in credit card charges accrued by a customer over the past year does this simple linear regression model explain? c. Estimate the corresponding simple linear regression with the customers number of years of posthigh school education as the independent variable and credit card charges accrued by a customer over the past year as the dependent variable. Interpret the estimated relationship between the customers number of years of posthigh school education and credit card charges accrued over the past year. How much variation in credit card charges accrued by a customer over the past year does this simple linear regression model explain? d. Recall the multiple regression in Figure 4.23 with credit card charges accrued by a customer over the past year as the dependent variable and customers annual household income (x1), number of members of the household (x2), and number of years of posthigh school education (x3) as the independent variables. Do the estimated slopes differ substantially from the corresponding slopes that were estimated using simple linear regression in parts a, b, and c? What does this tell you about multicollinearity in the multiple regression model in Figure 4.23? e. Add the coefficients of determination for the simple linear regression in parts a, b, and c, and compare the result to the coefficient of determination for the multiple regression model in Figure 4.23. What does this tell you about multicollinearity in the multiple regression model in Figure 4.23? f. Add age, a dummy variable for gender, and a dummy variable for whether a customer has exceeded his or her credit limit in the past 12 months as independent variables to the multiple regression model in Figure 4.23. Code the dummy variable for gender as 1 if the customers gender is female and 0 if male, and code the dummy variable for whether a customer has exceeded his or her credit limit in the past 12 months as 1 if the customer has exceeded his or her credit limit in the past 12 months and 0 otherwise. Do these variables substantially improve the fit of your model?
According to Thomson Financial, last year the majority of companies reporting profits had beaten estimates. A sample of 162 companies showed that 104 beat estimates, 29 matched estimates, and 29 fell short. What is the point estimate of the proportion that fell short of estimates? Determine the margin of error and provide a 95% confidence interval for the proportion that beat estimates. How large a sample is needed if the desired margin of error is 0.05?
The average annual premium for automobile insurance in the United States is 1,503. The following annual premiums () are representative of the web sites findings for the state of Michigan. Assume the population is approximately normal. a. Provide a point estimate of the mean annual automobile insurance premium in Michigan. b. Develop a 95% confidence interval for the mean annual automobile insurance premium in Michigan. c. Does the 95% confidence interval for the annual automobile insurance premium in Michigan include the national average for the United States? What is your interpretation of the relationship between auto insurance premiums in Michigan and the national average?
Based on a 90% confidence level, how many exceptions in backtesting a VAR would be expected over a 250-day trading year? a. 10 b. 15 c. 25 d. 50 Continuing with the previous question, what is the annualized rate of return earned on a cash-and-carry trade entered into in March and closed out in June? a. 9.8% b. 8.9% c. 39.1% d. 35.7%
By how many years did the Sarbanes-Oxley Act increase the potential prison sentence for fraud? a. 25 b. 10 c. 15 d. 5
Senior management of Nancy's Nooks (NN) has determined there is a 20 percent chance EPS will be $7.50 next year, there is a 60 percent chance EPS will be $3.00, and there is a 20 percent chance EPS will be -$3.70. Calculate the expected value, standard deviation, and coefficient of variation for NN's forecasted EPS. Do not round intermediate calculations. Round your answers for the expected value and standard deviation to the nearest cent and for the coefficient of variation to two decimal places. Expected value: $ Standard deviation: $ Coefficient of variation:
Monique invested in a mutual fund 5 years ago. Her nominal returns were exactly 10% every year over that five-year period, while inflation averaged 2%. Which of the following statements regarding average returns and standard deviation is most accurate? Group of answer choices: The real return on her investment is 10% The geometric average equals the arithmetic average The returns are positively skewed The standard deviation of returns is equal to 10%
Can it be shown how to find it on the financial calculator!! The past five monthly returns for Kentucky Jelly are 3.25 percent, 7.13 percent, -3.05 percent, 4.25 percent, and 6.75 percent. What is the standard deviation? 1.40 percent 3.37 percent 4.10 percent 16.83 percent
You invested $90,000 in a mutual fund at the beginning of the year when the NAV was $54.3. At the end of the year, the fund paid $.40 in short-term distributions and $.57 in long-term distributions. If the NAV of the fund at the end of the year was $63.94, what was your return for the year? (A negative value should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)