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free/or 0.5$ |
| m203 | An economist uses the price of a gallon of milk as a measure of inflation. She finds that the average price is $3.50 per gallon and the population standard deviation is $0.33. You decide to sample 40 convenience stores, collect their prices for a gallon of milk, and compute the mean price for the sample.
a. What is the standard error of the mean in this experiment?
b. What is the probability that the sample mean is between $3.46 and $3.54?
c. What is the probability that the difference between the sample mean and the population mean is less than $0.01?
d. What is the likelihood the sample mean is greater than $3.60? |
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| m204 | An Environmental Protection Agency study of 12 automobiles revealed a correlation of 0.47 between engine size and emissions. At the .01 significance level, can we conclude that there is a positive association between these variables? What is the p-value? Interpret. |
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| m205 | An industrial psychologist selected a random sample of seven young urban professional couples who own their homes. The size of their home (square feet) is compared with that of their parents. At the .05 significance level, can we conclude that the professional couples live in larger homes than theirparents? |
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| m206 | An insurance company, based on past experience, estimates the mean damage for a natural disaster in its area is $5,000. After introducing several plans to prevent loss, it randomly samples 200 policyholders and finds the mean amount per claim was $4,800 with a standard deviation of $1,300. Does it appear the prevention plans were effective in reducing the mean amount of a claim? Use the .05 significance level. |
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| m207 | An internal study by the Technology Services department at Lahey Electronics revealed company employees receive an average of two non-work-related e-mails per hour. Assume the arrival of these e-mails is approximated by the Poisson distribution.
a. What is the probability Linda Lahey, company president, received exactly one non-work-related e-mail between 4 p.m. and 5 p.m. yesterday?
b. What is the probability she received five or more non-work-related e-mails during the same period?
c. What is the probability she did not receive any non-work-related e-mails during the period? |
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| m208 | An investigation of the effectiveness of an antibacterial soap in reducing operating room contamination resulted in the accompanying table. The new soap was tested in a sample of eight operating rooms in the greater Seattle area during the last year. The following table reports the contamination levels before and after the use of the soap for each operating room.
At the .05 significance level, can we conclude the contamination measurements are lower after use of the newsoap? |
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| m209 | An investment advisor is studying the relationship between a common stock’s price to earnings (P/E) ratio and factors that she thinks would influence it. She has the following data on the earnings per share (EPS) and the dividend percentage (Yield) for a sample of 20 stocks.
a. Develop a multiple linear regression with P/E as the dependent variable.
b. Are either of the two independent variables an effective predictor of P/E?
c. Interpret the regression coefficients.
d. Do any of these stocks look particularly undervalued?
e. Plot the residuals and check the normality assumption. Plot the fitted values against the residuals.
f. Does there appear to be any problems with homoscedasticity?
g. Develop a correlation matrix. Do any of the correlations indicatemulticollinearity? |
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| m210 | An investor believes there is a 50–50 chance that a stock will increase on a particular day. To investigate this idea, for 30 consecutive trading days the investor selects a random sample of 50 stocks and counts the number that increase. The number of stocks in the sample that increased is reported below.
Develop p-chart and write a brief report summarizing your findings. Based on these sample results, is it reasonable that the odds are 50–50 that a stock will increase? What percent of the stocks would need to increase in a day for the process to be “out ofcontrol”? |
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| m211 | An investor buys 100 shares of AT&T stock and records its price change daily.
a. List several possible events for this experiment.
b. Which concept of probability did you use in (a)? |
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| m212 | An investor owns three common stocks. Each stock, independent of the others, has equally likely chances of (1) increasing in value, (2) decreasing in value, or (3) remaining the same value. List the possible outcomes of this experiment. Estimate the probability at least two of the stocks increase in value. |
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| m213 | An investor purchased 100 shares of Fifth Third Bank stock and 100 shares of Santee Electric Cooperative stock. The probability the bank stock will appreciate over a year is .70. The probability the electric utility will increase over the same period is .60. Assume the two events are independent.
a. What is the probability both stocks appreciate during the period?
b. What is the probability the bank stock appreciates but the utility does not?
c. What is the probability at least one of the stocks appreciates? |
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| m214 | An urban planner claims that, nationally, 20% of all families renting condominiums move during a given year. A random sample of 200 families renting condominiums in the Dallas Metroplex revealed that 56 moved during the past year. At the .01 significance level, does this evidence suggest that a larger proportion of condominium owners moved in the Dallas area? Determine the p-value. |
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| m215 | Answer the following questions in one or two well-constructed sentences.
a. What happens to the standard error of the mean if the sample size is increased?
b. What happens to the distribution of the sample means if the sample size is increased?
c. When using the distribution of sample means to estimate the population mean, what is the benefit of using larger sample sizes? |
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| m216 | Appendix B.4 is a table of random numbers that are uniformly distributed. Hence, each digit from 0 to 9 has the same likelihood of occurrence.
a. Draw a graph showing the population distribution of random numbers. What is the population mean?
b. Following are the first 10 rows of five digits from the table of random numbers in Appendix B.4. Assume that these are 10 random samples of five values each. Deter minethe mean of each sample and plot the means on a chart similar to Chart 8–4. Compare the mean of the sampling distribution of the sample mean with the populationmean. |
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| m217 | An apple juice bottling company maintains records concerning the number of unacceptable bottles of juice obtained from the filling and capping machines. Based on past data, the probability that a bottle came from machine I and was nonconforming is 0.05 and the probability that a bottle came from machine II and was nonconforming is 0.075. These probabilities represent the probability of one bottle out of the total sample having the specified characteristics. Half the bottles are filled on machine I and the other half are filled on machine II.
a. If a filled bottle of juice is selected at random, what is the probability that it is a nonconforming bottle?
b. If a filled bottle of juice is selected at random, what is the probability that it was filled on machine II?
c. If a filled bottle of juice is selected at random, what is the probability that it was filled on machine I and is a conforming bottle? |
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| m218 | Appliance Center sells a variety of electronic equipment and home appliances. For the last 4 years, 2010 through 2013, the following quarterly sales (in $ millions) were reported.
Determine a typical seasonal index for each of the fourquarters. |
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| m219 | Applying the generalized divergence theorem to the set M = {XЄrN: |x| < a} and , find the volume of Sn – 1 = {xЄRn: |x| = 1} in terms of the -dimensional volume of Bn = {x Є Rn: |x| <1}. (This volume is π n/2 / (n/2)! if is even and 2(n+1)/2π (n-1)/2 1∙3∙5∙. ∙ N if is odd.) |
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| m220 | Arbitron Media Research Inc. conducted a study of the iPod listening habits of men and women. One facet of the study involved the mean listening time. It was discovered that the mean listening time for men was 35 minutes per day. The standard deviation of the sample of the 10 men studied was 10 minutes per day. The mean listening time for the 12 women studied was also 35 minutes, but the standard deviation of the sample was 12 minutes. At the .10 significance level, can we conclude that there is a difference in the variation in the listening times for men and women? |
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| m221 | Armco, a manufacturer of traffic light systems, found that under accelerated-life tests, 95% of the newly developed systems lasted 3 years before failing to change signals properly. a. If a city purchased four of these systems, what is the probability all four systems would operate properly for at least 3 years?
b. Which rule of probability does this illustrate?
c. Using letters to represent the four systems, write an equation to show how you arrived at the answer to part (a). |
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| m222 | As a condition of employment, Fashion Industries applicants must pass a drug test. Of the last 220 applicants, 14 failed the test. Develop a 99% confidence interval for the proportion of applicants who fail the test. Would it be reasonable to conclude that 10% of the applicants fail the test? Explain. |
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