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free/or 0.5$ |
| m6828 | A random variable X is normally distributed with a mean of 100 and a variance of 100, and a random variable Y is normally distributed with a mean of 200 and a variance of 400. The random variables have a correlation coefficient equal to 0.5. Find the mean and variance of the random variable:
W = 5X - 4Y |
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| m6829 | A random variable X is normally distributed with a mean of 100 and a variance of 500 and a random variable Y is normally distributed with a mean of 200 and a variance of 400. The random variables have a correlation coefficient equal to -0.5. Find the mean and variance of the random variable:
W = 5X - 4Y |
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| m6830 | A random variable X is normally distributed with a mean of 500 and a variance of 100 and a random variable Y is normally distributed with a mean of 200 and a variance of 400. The random variables have a correlation coefficient equal to 0.5. Find the mean and variance of the random variable:
W = 5X - 4Y |
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| m6831 | A real estate agent hypothesizes that in her town the selling price of a house in dollars (y) depends on its size in square feet of floor space (x1), the lot size in square feet (x2), the number of bedrooms (x3), and the number of bathrooms 1x42. For a random sample of 20 house sales, the following least squares estimated model was obtained:
The numbers in parentheses under the coefficients are the estimated coefficient standard errors.
a. Interpret in the context of this model the estimated coefficient on x2.
b. Interpret the coefficient of determination.
c. Assuming that the model is correctly specified, test, at the 5% level against the appropriate onesided alternative, the null hypothesis that, all else being equal, selling price does not depend on number of bathrooms.
d. Estimate the selling price of a house with 1,250 square feet of floor space, a lot of 4,700 square feet, 3 bedrooms, and 1 bathroom. |
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| m6832 | A real estate agent is interested in the relationship between the number of lines in a newspaper advertisement for an apartment and the volume of inquiries from potential renters. Let volume of inquiries be denoted by the random variable X, with the value 0 for little interest, 1 for moderate interest, and 2 for strong interest. The real estate agent used historical records to compute the joint probability distribution shown in the accompanying table.
a. Find the joint cumulative probability at X = 1, Y = 4, and interpret your result.
b. Find and interpret the conditional probability distribution for Y, given X = 0.
c. Find and interpret the conditional probability distribution for X, given Y = 4.
d. Find and interpret the covariance between X and Y.
e. Are number of lines in the advertisement and volume of inquiries independent of one another? |
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| m6833 | A recent radio commentator argued that his experience indicated that women believed that purchasing higher-cost food would improve their lifestyle. Is there evidence to conclude that women have a lower daily food cost compared to men (daily-cost)? Use an appropriate test to determine the answer. You will do the analysis based first on the data from the first interview, creating subsets of the data file using daycode = 1, and a second time using data from the second interview, creating subsets of the data file using daycode = 2. |
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| m6834 | A recent report from a health concerns study indicated that there is strong evidence of a nation s overall health decay if the percent of obese adults exceeds 28%. In addition, if the low-income preschool obesity rate exceeds 13%, there is great concern about long-term health. You are asked to conduct an analysis to determine if there is a difference in these two obesity rates in metro versus nonmetro counties.
Use the data file Food Nutrition Atlas-described in the Chapter 9 appendix-as the basis for your statistical analysis. Prepare a rigorous analysis and a short statement that reports your statistical results and your conclusions. |
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| m6835 | A recent report from a health concerns study indicated that there is strong evidence of a nation s overall health decay if the percent of obese adults exceeds 28%. In addition, if the low-income preschool obesity rate exceeds 13%, there is great concern about long-term health. You are asked to conduct an analysis to determine if there is a difference in these two obesity rates in metro versus nonmetro counties. Your analysis is restricted to counties in the following states; California, Michigan, Minnesota, and Florida. Conduct your analysis for each state. Use the data file Food Nutrition Atlas-described in the Chapter 9 appendix-as the basis for your statistical analysis. You will first need to obtain a subset of the data file using the capabilities of your statistical analysis computer program.
Prepare a rigorous analysis and a short statement that reports your statistical results and your conclusions. |
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| m6836 | A recent report from a health-concerns study indicated that there is strong evidence of a nation s overall health decay if the percent of obese adults exceeds 28%. In addition, if the low-income preschool obesity rate exceeds 13%, there is great concern about long-term health. You are asked to conduct an analysis to determine if the U.S. population exceeds that rate. Your analysis is restricted to those counties where the adult participation in physical activity exceeds 64.3%. To do this you will first need to obtain a subset of the data file using the capabilities of your statistical analysis computer program. Use the data file Food Nutrition Atlas as the basis for your statistical analysis. Variable descriptions are located in the chapter appendix. Prepare a rigorous analysis and a short statement that reports your statistical results and your conclusions. |
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| m6837 | A recent report from a health-concerns study indicated that there is strong evidence of a nation s overall health decay if the percent of obese adults exceeds 28%. In addition, if the low-income preschool obesity rate exceeds 13%, there is great concern about long-term health. You are asked to conduct an analysis to determine if the U.S. population exceeds that rate. Your analysis is restricted to those counties in the following states: California, Michigan, Minnesota, and Florida. Conduct your analysis for each state. To do this, you will first need to obtain a subset of the data file using the capabilities of your statistical analysis computer program.
Use the data file Food Nutrition Atlas as the basis for your statistical analysis. Variable descriptions are located in the chapter appendix. Prepare a rigorous analysis and a short statement that reports your statistical results and your conclusions.
Nutrition Research-Based Exercises
The Economic Research Service (ERS), a prestigious think tank research center in the U.S. Department of Agriculture, is conducting a series of research studies to determine the nutrition characteristics of people in the United States. This research is used for both nutrition education and government policy designed to improve personal health. See for example, Carlson, A, et al. 2010.
The data file HEI Cost Data Variable Subset contains considerable information on randomly selected individuals who participated in an extended interview an |
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| m6838 | A recent report from a study of health concerns indicated that there is strong evidence of a nation s overall health decay if the percent of obese adults exceeds 28%. In addition, if the low-income preschool obesity rate exceeds 13%, there is great concern about long-term health. You are asked to conduct an analysis to determine if the U.S. population exceeds that rate. Use the data file Food Nutrition Atlas as the basis for your statistical analysis. Variable descriptions are located in the chapter appendix. Prepare a rigorous analysis and a short statement that reports your statistical results and your conclusions. |
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| m6839 | A record store owner finds that 20% of customers entering her store make a purchase. One morning 180 people, who can be regarded as a random sample of all customers, enter the store.
a. What is the mean of the distribution of the sample proportion of customers making a purchase?
b. What is the variance of the sample proportion?
c. What is the standard error of the sample proportion?
d. What is the probability that the sample proportion is less than 0.15? |
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| m6840 | A record-store owner assesses customers entering the store as high school age, college age, or older, and finds that of all customers 30%, 50%, and 20%, respectively, fall into these categories. The owner also found that purchases were made by 20% of high school age customers, by 60% of college age customers, and by 80% of older customers.
a. What is the probability that a randomly chosen customer entering the store will make a purchase?
b. If a randomly chosen customer makes a purchase, what is the probability that this customer is high school age? |
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| m6841 | A regression analysis has produced the following analysis of variance table:
a. Compute se and s2ε.
b. Compute SST.
c. Compute R2 and the adjusted coefficient of determination. |
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| m6842 | A regression analysis has produced the following analysis of variance table:
a. Compute se and s2ε.
b. Compute SST.
c. Compute R2 and the adjusted coefficient of determination. |
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| m6843 | A regression analysis has produced the following analysis of variance table:
a. Compute se and s2ε.
b. Compute SST.
c. Compute R2 and the adjusted coefficient of determination. |
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| m6844 | A regression analysis has produced the following analysis of variance table:
a. Compute se and s2ε.
b. Compute SST.
c. Compute R2 and the adjusted coefficient of determination. |
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| m6845 | A regression model of total grocery sales on disposable income was estimated using data from small, isolated towns in the western United States. Prepare a list of factors that might contribute to the random error term. |
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| m6846 | A regression model was estimated to compare performance of students taking a business statistics course—either as a standard 14-week course or as an intensive 3-week course. The following model was estimated from observations of 350 students (Van Scyoc and Gleason 1993):
where
y` = score on a standardized test of understanding of statistics after taking the course
x1 = dummy variable taking the value 1 if the 3-week course was taken and 0 if the 14-week course was taken
x2 = student s grade point average
x3 = dummy variable taking the value 0 or 1, depending on which of two teachers had taught the course
x4 = dummy variable taking the value 1 if the student is male and 0 if female
x5 = score on a standardized test of understanding of mathematics before taking the course
x6 = number of semester credit hours the student had completed
x7 = age of student
The numbers in parentheses under the coefficients are the estimated coefficient standard errors. Write a report discussing what can be learned from this fitted regression. |
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| m6847 | A research group wants to estimate the proportion of consumers who plan to buy a scanner for their PC during the next 3 months.
a. How many people should be sampled so that the sampling error is at most 0.04 with a 90% confidence interval?
b. What is the sample size required if the confidence is increased to 95%, keeping the sampling error the same?
c. What is the required sample size if the research group extends the sampling error to 0.05 and wants a 98% confidence level? |
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