Chapter 6:
6.2- Number the rows in the Excel file Credit Risk Data to identify each record. The bank wants to sample from this database to conduct a more detailed audit. Use the Excel Sampling tool to find a simple random sample of 20 unique records.
6.6- Find point estimates for the mean and standard deviation of the Months Customer data in the Credit Risk Data file. Draw five random samples of sizes 50 and 250 from the data using the Sampling tool. Use the empirical rules to analyze the sampling error and state your conclusions.
6.11- In determining automobile mileage ratings, it was found that the mpg in the city for a certain model is normally distributed, with a mean of 30 mpg and a standard deviation of 1.7 mpg. Suppose that the car manufacturer samples five cars from its assembly line and tests them for mileage ratings.
a. What is the distribution of the mean mpg for the sample?
b. What is the probability that the mean mpg of the sample will be greater than 31 mpg?
c. What is the probability that the mean mpg of the sample will be less than 29.5 mpg?
6.13- From a sample of 22 graduate students, the mean number of months of work experience prior to entering an MBA program was 34.86. The national standard deviation is known to be 19 months. What is a 95% confidence interval for the population mean? Compute the confidence interval using the appropriate formula and verify your results using the Excel Confidence Intervals template.
6.15- A survey of 26 college freshmen found that they average 6.85 hours of sleep each night. A 90% confidence interval had a margin of error of 0.497.
a. What are the lower and upper limits of the confidence interval?
b. What was the standard deviation, assuming that the population standard deviation is known?
6.18- A survey of 23 individuals found that they spent an average of $39.48 on headphones to use for exercising. The margin of error for a 95% confidence interval was found to be 21.2.
a. What are the lower and upper limits of the confidence interval?
b. What was the standard deviation of the sample?
6.19- For the data in the Excel file Grade Point Averages, find 90%, 95%, and 99% confidence intervals for the mean GPA. Compute the confidence intervals using the appropriate formulas and verify your results using the Excel Confidence Intervals template.
6.20- For the data in the Excel file Debt and Retirement Savings, find 95% confidence intervals for the mean income, long-term debt, and retirement savings. Use the appropriate formulas and Excel functions.
Chapter 7:
7- The price of a certain combo meal at different franchises of a national fast food company varies from $5.00 to $7.36 and has a known standard deviation of $2.11. A sample of 23 students in an online course that includes students across the country stated that their average price is $5.75. The students have also stated that they are generally unwilling to pay more than $6.50 for this meal. Formulate and conduct a hypothesis test to determine if you can conclude that the population mean is less than $6.50.
8- A business school has a goal that the average number of years of work experience of its MBA applicants is more than three years. Historical data suggest that the variance has been constant at around six months, and thus, the population variance can be assumed to be known. Based on last year’s applicants, it was found that among a sample of 47, the average number of years of work experience is 3.1. Can the school state emphatically that it is meeting its goal? Formulate the appropriate hypothesis test and conduct the test.
9- According to a magazine, people read an average of more than two books in a month. A survey of 25 random individuals found that the mean number of books they read was 2.1 with a standard deviation of 1.24.
a. To test the magazine’s claim, what should the appropriate hypotheses be?
b. Compute the test statistic.
c. Using a level of significance of 0.05, what is the critical value?
d. Find the p-value for the test.
e. What is your conclusion?
10- A national poll stated that most Americans exercise more than two days a week. A random sample of 105 Americans found that the average number of days they exercised each week was 2.17, with a standard deviation of 2.14. Is there sufficient evidence to support the poll results? Formulate the appropriate hypothesis test and draw a conclusion.
11- A bank found that in recent years, the average monthly charge on its credit card was $1,350. With an improving economy, they suspect that this amount has increased. A sample of 42 customers resulted in an average monthly charge of $1,376.54 with a standard deviation of $183.89. Do these data provide statistical evidence that the average monthly charge has increased? Formulate the appropriate hypothesis test and draw a conclusion.
12- Using the data in the Excel file Consumer Transportation Survey, test the following null hypotheses:
a. Individuals spend at least eight hours per week in their vehicles.
b. Individuals drive an average of 600 miles per week.
c. The average age of SUV drivers is no greater than 35.
d. At least 80% of individuals are satisfied with their vehicles.
Perform the calculations using the correct formulas and Excel functions, and compare your results with the One Sample Hypothesis Test Excel template to verify them.
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Chapter 8:
- Using the data in the Excel file Demographics, determine if a linear relationship exists between unemployment rates and cost of living indexes by constructing a scatter chart. Visually, do there appear to be any outliers? If so, delete them and then find the best-fitting function using the Trendline tool. What would you conclude about the strength of any relationship?
- Use the data in the Excel file MBA Motivation and Salary Expectations to determine how well a linear function models the relationship between pre- and post-MBA salaries. Compare it to a third-order polynomial. Would the polynomial model have a logical explanation?
- Using the data in the Excel file Weddings, construct scatter charts to determine whether any linear relationship appears to exist between (1) the wedding cost (X) and attendance (Y), (2) the wedding cost (X) and the value rating (Y), and (3) the couple’s income (X) and wedding cost (Y) only for the weddings paid for by the bride and groom. Then find the best-fitting functions using the Trendline tool for each of these charts.