SCORE 100%
Question 1: Exercise 09.03 (Developing Null and Alternative Hypotheses)
A production line operation is designed to fill cartons with laundry detergent to a mean weight of ounces. A sample of cartons is periodically selected and weighed to determine whether underfilling or overfilling is occurring. If the sample data lead to a conclusion of underfilling or overfilling, the production line will be shut down and adjusted to obtain proper filling.
a. Formulate the null and alternative hypotheses that will help in deciding whether to shut down and adjust the production line.
b. Comment on the conclusion when cannot be rejected. Is there evidence that the production line is not operating properly?
c. Comment on the conclusion when can be rejected. Can we conclude that overfilling or underfilling exists?
Question 2 Exercise 09.07 (Type I and Type II Errors)
Carpetland salespersons average per week in sales. Steve Contois, the firm's vice president, proposes a compensation plan with new selling incentives. Steve hopes that the results of a trial selling period will enable him to conclude that the compensation plan increases the average sales per salesperson.
a. Develop the appropriate null and alternative hypotheses.
:
:
b. What is the Type I error in this situation?
In this situation, a Type I error would occur if it was concluded that the new compensation plan provides a population mean weekly sales
when in fact it does not.
What are the consequences of making this error?
c. What is the Type II error in this situation?
In this situation, a Type II error would occur if it was concluded that the new compensation plan provides a population mean weekly sales
when in fact it does not.
What are the consequences of making this error?
Question 3 Exercise 09.19 (Population Mean: Sigma Known)
According to the IRS, taxpayers calling the IRS in waited minutes on average for an IRS telephone assister to answer. Do callers who use the IRS help line early in the day have a shorter wait? Suppose a sample of callers who placed their calls to the IRS in the first minutes that the line is open during the day have a mean waiting time of minutes before an IRS telephone assister answers. Based on data from past years, you decide that it is reasonable to assume that the standard deviation of waiting times is minutes. Using these sample results, can you conclude that the waiting time for calls placed during the first minutes the IRS help line is open each day is significantly less than the overall mean waiting time of minutes? Use .
State the hypotheses.
: What is the p-value (to decimals)?
Can you conclude that callers who use the IRS help-line early in the day have a shorter wait?
Question 4 Exercise 09.29 (Population Mean: Sigma Unknown)
On its municipal website, the city of Tulsa states that the rate it charges per CCF of residential water is . How do the residential water rates of other U.S. public utilities compare to Tulsa's rate? The file ResidentialWater contains the rate per CCF of residential water for randomly selected U.S. cities.
Click on the datafile logo to reference the data.
a. Formulate hypotheses that can be used to determine whether the population mean rate per CCF of residential water charged by U.S. public utilities differs from the rate charged by Tulsa.
Choose the correct null hypothesis:
1. :
2. :
3. :
Choose the correct alternative hypothesis:
1. :
2. :
3. :
b. What is the -value for your hypothesis test in part (a)? Round your answer to four decimal places.
c. At , can your null hypothesis be rejected? What is your conclusion?
the null hypothesis. The mean rate per CCF of residential water throughout the U.S.
significantly from the rate per CCF of residential water in Tulsa.
d. Repeat the preceding hypothesis test using the critical value approach.
The critical value(s) is(are)
.
= (to decimals),
the null hypothesis.
Question 5 Exercise 09.43 (Population Proportion)
Eagle Outfitters is a chain of stores specializing in outdoor apparel and camping gear. They are considering a promotion that involves mailing discount coupons to all its credit card customers. This promotion will be considered a success if more than of those receiving the coupons use them. Before going national with the promotion, coupons were sent to a sample of credit card customers.
Click on the datafile logo to reference the data.
a. Develop hypotheses that can be used to test whether the population proportion of those who will use the coupons is sufficient to go national.
:
:
b. The file Eagle contains the sample data. Develop a point estimate of the population proportion (to decimals).
c. Use to conduct your hypothesis test. Should Eagle go national with the promotion?
Question 6 Exercise 09.51 (Population Mean: Sigma Known)
At Western University the historical mean of scholarship examination scores for freshman applications is . A historical population standard deviation is assumed known. Each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed.
a. State the hypotheses.
:
:
b. What is the confidence interval estimate of the population mean examination score if a sample of applications provided a sample mean of (to the nearest whole number)?
( , )
c. Use the confidence interval to conduct a hypothesis test. Using , can the assistant dean conclude that the mean examination score for the new freshman applications has changed?
d. What is the -value (to decimals)? (Use Table 1 from Appendix B.)
Question 7 Exercise 09.57 (Population Mean: Sigma Unknown)
According to the National Association of Realtors, it took an average of three weeks to sell a home in . Data for the sale of randomly selected homes sold in Greene County, Ohio, in showed a sample mean of weeks with a sample standard deviation of weeks. Conduct a hypothesis test to determine whether the number of weeks until a house sold in Greene County differed from the national average in . Round your answer to four decimal places.
p-value =
Use for the level of significance, and state your conclusion.
- Reject . There is a statistically significant difference between the national average time to sell a home and the mean time to sell a home in Greene County.
- Reject . There is not a statistically significant difference between the national average time to sell a home and the mean time to sell a home in Greene County.
- Do not reject . There is a statistically significant difference between the national average time to sell a home and the mean time to sell a home in Greene County.
- Do not reject . There is not a statistically significant difference between the national average time to sell a home and the mean time to sell a home in Greene County.
Choose the correct option.
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