- Use two-step procedure to select a simple random sample of EAI employees.
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
177
2. According to Wine-Searcher, wine critics generally use a wine-scoring scale to communicate their opinions on the relative quality of wines. Wine scores range from to , with a score of indicating a great wine, indicating an outstanding wine, indicating a very good wine, indicating a good wine, indicating a mediocre wine, and below indicating that the wine is not recommended. Random ratings of a pinot noir recently produced by a newly established vineyard in follow:
| 87 | 91 | 86 | 82 | 72 | 91 |
| 60 | 77 | 80 | 79 | 83 | 96 |
a. Develop a point estimate of mean wine score for this pinot noir (to decimals).
82.0
b. Develop a point estimate of the standard deviation for wine scores received by this pinot noir (to decimals).
9.6389
3. In , the Pew Internet & American Life Project asked teens aged to several questions about their attitudes toward social media. The results showed that say social media makes them feel more connected to what is going on in their friends’ lives; say social media helps them interact with a more diverse group of people; and feel pressure to post content that will get a lot of likes and comments.
a. Develop a point estimate of the proportion of teens aged to who say social media makes them feel more connected to what is going on in their friends’ lives.
0.8102
b. Develop a point estimate of the proportion of teens aged to who say social media helps them interact with a more diverse group of people.
0.6904
c. Develop a point estimate of the proportion of teens aged to who feel pressure to post content that will get a lot of likes and comments.
0.3701
4. The CPA Practice Advisor reports that the mean preparation fee for federal income tax returns was . Use this price as the population mean and assume the population standard deviation of preparation fees is . Use z-table.
Round your answers to four decimal places.
a. What is the probability that the mean price for a sample of federal income tax returns is within of the population mean?
0.6212
b. What is the probability that the mean price for a sample of federal income tax returns is within of the population mean?
0.7416
c. What is the probability that the mean price for a sample of federal income tax returns is within of the population mean?c
0.8904
None of the sample sizes in parts (a), (b), and (c) are large enough.
4. The Food Marketing Institute shows that of households spend more than per week on groceries. Assume the population proportion is and a simple random sample of households will be selected from the population. Use the z-table.
a. Show the sampling distribution of , the sample proportion of households spending more than per week on groceries.
0.17
0.0133
b. What is the probability that the sample proportion will be within of the population proportion (to decimals)?
0.8679
0.9668
5. A simple random sample of items resulted in a sample mean of . The population standard deviation is .
a. Compute the confidence interval for the population mean. Round your answers to one decimal place.
76.20 83.80
b. Assume that the same sample mean was obtained from a sample of items. Provide a confidence interval for the population mean. Round your answers to two decimal places.
77.32 82.68
c. What is the effect of a larger sample size on the interval estimate?
Smaller
6. For a t distribution with degrees of freedom, find the area, or probability, in each region.
a. To the right of
0.025
b. To the left of
0.90
c. To the left of
0.05
d. To the right of
0.01
e. Between and
0.95
f. Between and
0.90
7. Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and prepreview ads before the movie starts. Many complain that the time devoted to previews is too long. A preliminary sample conducted by The Wall Street Journal showed that the standard deviation of the amount of time devoted to previews was 4 minutes. Use that as a planning value for the standard deviation in answering the following questions. Round your answer to next whole number.
a. If we want to estimate the population mean time for previews at movie theaters with a margin of error of seconds, what sample size should be used? Assume confidence.
40
b. If we want to estimate the population mean time for previews at movie theaters with a margin of error of minute, what sample size should be used? Assume confidence.
62
8. Fewer young people are driving. In , of people under years old who were eligible had a driver’s license. Bloomberg reported that percentage had dropped to in . Suppose these results are based on a random sample of people under years old who were eligible to have a driver’s license in and again in .
a. At confidence, what is the margin of error and the interval estimate of the number of eligible people under years old who had a driver’s license in ?
0.0272
0.6118 0.6662
b. At confidence, what is the margin of error and the interval estimate of the number of eligible people under years old who had a driver’s license in ?
0.0279
0.3891 0.4449
c. Is the margin of error the same in parts (a) and (b)?
No
Why, or why not?
Option 1
8. The Centers for Disease Control and Prevention (CDC) defines a healthy sleep duration to be at least seven hours per day. The CDC reports that the percentage of people who report a healthy sleep duration varies by marital status. The CDC also reports that in , of those who are married report a healthy sleep duration; of those who have never been married report a healthy sleep duration; and of those who are divorced, widowed, or separated report a healthy sleep duration. The file SleepHabits contains sample data on the sleeping habits of people who have never been married that are consistent with the CDC’s findings. Use these data to answer the following questions. Click on the datafile logo to reference the data.
a. Develop a point estimate and a confidence interval for the proportion of those who have never been married who report a healthy sleep duration.
0.63
0.61872 0.6413
b. Develop a point estimate and a confidence interval for the mean number of hours of sleep for those who have never been married.
7.2257
7.2065 7.2449
c. For those who have never been married, estimate the number of hours of sleep per day for those who report a healthy sleep duration (to decimals).
7.7293
9. The National Center for Education Statistics reported that of college students work to pay for tuition and living expenses. Assume that a sample of college students was used in the study.
a. Provide a confidence interval for the population proportion of college students who work to pay for tuition and living expenses. (to decimals)
0.42 0.52
b. Provide a confidence interval for the population proportion of college students who work to pay for tuition and living expenses. (to decimals)
0.41 0.53
c. What happens to the margin of error as the confidence is increased from to ?
larger
10. The manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a weekend is or less. A member of the hotel’s accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of future weekend guest bills to test the manager’s claim.
a. Which form of the hypotheses should be used to test the manager’s claim?
less than or equal to 600
greater than 600
b. When cannot be rejected, can we conclude that the manager’s claim is wrong?
NO
c. When can be rejected, can we conclude that the manager’s claim is wrong?
Yes
11. 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.
Equal 32
Not equal 32
b. Comment on the conclusion when cannot be rejected. Is there evidence that the production line is not operating properly?
NO allow production to continue
c. Comment on the conclusion when can be rejected. Can we conclude that overfilling or underfilling exists?
Yes adjust the production line
12. 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.
less than or equal to 8000
greater than 8000
b. What is the Type I error in this situation?
greater than 8000
What are the consequences of making this error?
This could lead to implementing the plan when it does not help.
c. What is the Type II error in this situation?
less than or equal to 8000
What are the consequences of making this error?
This could lead to not implementing a plan that would increase sales.
13. Consider the following hypothesis test:
A sample of is used and the population standard deviation is . Use the critical value approach to state your conclusion for each of the following sample results. Use .
Note: In the following questions, if the correct option is “Reject ” select “option 1” . If “Do not reject ” is correct, then select “option 2”.
a. Option 1
b. option 2
c. option 1
14. TextRequest reports that adults years old send and receive texts every day. Suppose we take a sample of year olds to see if their mean number of daily texts differs from the mean for year olds reported by TextRequest.
a. Select the null hypothesis we should use to test whether the population mean daily number of texts for year olds differs from the population daily mean number of texts for year olds.
1
Select the alternative hypothesis we should use to test whether the population mean daily number of texts for year olds differs from the population daily mean number of texts for year olds.
1
b. Suppose a sample of thirty year olds showed a sample mean of texts per day. Assume a population standard deviation of texts per day and compute the -value. Round your answer to four decimal places.
0.1206
c. With as the level of significance, what is your conclusion?
Do not reject cannot
d. Repeat the preceding hypothesis test using the critical value approach.
+/-1.96
Can it be concluded that the population mean differs from ?
No
15. 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 .
Option 2
Option 3
What is the -value (to decimals)?
0.0384
Can you conclude that callers who use the IRS help-line early in the day have a shorter wait?
Yes
16. Consider the following hypothesis test:
A sample of provided a sample mean and a sample standard deviation .
a. Compute the value of the test statistic (to decimals).
2.31
between 0.01 and 0.025
c. At , what is your conclusion?
Reject full hypothesis
d. What is the rejection rule using the critical value? (Use .)
greater than or equal to 1.711
Can you conclude that the population mean is greater than ?
Yes
17. Consider the following hypothesis test:
A sample of is used. Identify the -value and state your conclusion for each of the following sample results. Use .
a. With and , the -value is between 0.10 and 0.20
Can it be concluded that the population mean is less than ?
NO
b. With and , the -value is between 0.005 and 0.01
Can it be concluded that the population mean is less than ?
Yes
c. With and , the -value is Greater than 0.20
Can it be concluded that the population mean is less than ?
No
18. 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.
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.
1
Choose the correct alternative hypothesis:
1
b. What is the -value for your hypothesis test in part (a)? Round your answer to four decimal places.
0.2576
c. At , can your null hypothesis be rejected? What is your conclusion?
Do not reject
Does not differ
d. Repeat the preceding hypothesis test using the critical value approach.
The critical value(s) is(are) +/-2.02
-1.148 do not rejecrt
19. In , RAND Corporation researchers found that of all individuals ages to are adequately prepared financially for retirement. Many financial planners have expressed concern that a smaller percentage of those in this age group who did not complete high school are adequately prepared financially for retirement.
a. Develop appropriate hypotheses such that rejection of will support the conclusion that the proportion of those who are adequately prepared financially for retirement is smaller for people in the age group who did not complete high school than it is for the population of the age group.
greater than or equal to 0.71
Less than 0.71
b. In a random sample of people from the age group who did not complete high school, were not prepared financially for retirement. What is the -value for your hypothesis test (to decimals)? If your answer is zero, enter “0”.
0
c. At , what is your conclusion?
conclude that the percentage of year old individuals who are adequately prepared financially for retirement is smaller for those who did not complete high school.
20. 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.
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.
less than or equal to 0.10
greater than 0.10
b. The file Eagle contains the sample data. Develop a point estimate of the population proportion (to decimals).
0.13
c. Use to conduct your hypothesis test. Should Eagle go national with the promotion?
‘No, Eagle should not go national with the promotion: a larger sample should be taken
21. 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.
equal to 900
not equal to 900
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)?
910 960
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?
yes
d. What is the -value (to decimals)? (Use Table 1 from Appendix B.)
0.006
22. 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.
0.0652
Use for the level of significance, and state your conclusion.
I. 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.
II. 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.
III. 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.
IV. 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.
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