The Inference Portfolio - COMBS AP STATS STUFF



The Inference Portfolio

(Everything & anything you ever wanted to know about inference!)

• There are ten problems to complete. This will be graded as completion. Be sure to turn in on time.

• All work must be NEATLY shown with a full write-up.

• Portfolio should include a cover page and be in a folder.

o (I have spare folders for you to use)

• An in-class problem will be done on the due-date. This and two randomly chosen problems will be graded for correctness.

• Portfolio counts as a test grade.

Name: ______________________________

Inference Portfolio Grading Rubric

1. One Sample z completed __________

2. One Sample t completed __________

3. Matched Pairs t completed __________

4. One Sample Proportion z completed __________

5. Two sample t completed __________

6. Two Sample Proportion z completed __________

7. Chi-Square Goodness of Fit completed __________

8. Chi-Square Homogeneity completed __________

9. Chi-Square Independence completed __________

10. Linear Regression t on slope completed __________

11. Random problem correct __________

12. Random problem correct __________

13. In-class problem correct __________

14. Notebook, cover sheet, neatness __________

Total: ________

One Sample z

Radon is a colorless gas that is naturally released by rocks and soils and may concentrate in tightly closed houses. Because radon is slightly radioactive, there is come concern that it may be a health hazard. Radon detectors are sold to homeowners worried about this risk, but the detectors may be inaccurate. University researchers placed 12 detectors in a chamber where they were exposed to 105 Pico curies per liter of radon over 3 days. Here are the readings given by the detectors:

91.9 97.8 111.4 122.3 105.4 95.0

103.8 99.6 96.6 119.3 104.8 101.7

Assume (unrealistically) that you know that the standard deviation of readings for all detectors of this type is σ = 9. (Yates, Moore & McCabe, The Practice of Statistics, p. 555)

a) Give a 90% confidence interval for the mean reading μ for this type of detector.

b) Is there significant evidence at the 10% level that the mean reading differs from the true value of 105?

One Sample t

A preliminary study of the fall lobster catch showed that for 35 lobsters selected at random the mean weight was 2.9 pounds with standard deviation of 0.6 pounds. (Brase & Brase, Understandable Statistics – test item file p. 8-4)

a) Find a 90% confidence interval for the population mean weight of the fall lobsters.

b) How many more lobsters should be included in the sample if we want to say with 90% confidence that the population mean weight of the fall lobsters catch is within 0.1 pounds of the sample mean?

c) The mean weight for the lobster population during the past 10 years has been reported as 3.2 pounds. Does the preliminary study indicate that the mean weight of lobsters caught this year will be significantly different from past years?

Matched-Pairs t

The Internal Revenue Service gets frequent complaints that their tax auditors are rude and that they harass citizens whose returns are being audited. To try to improve public relations, the government conducted a one-day sensitivity training seminar for the auditors. A random sample of 10 auditors who participated in the seminar was selected. The data below show the number of complaints for each auditor in the sample for the month prior to the sensitivity training and for the month after the seminar.

Auditor 1 2 3 4 5 6 7 8 9 10

Before 5 7 2 3 8 9 6 4 10 3

After 3 8 3 2 5 7 7 5 9 4

Test the claim that the average number of complaints during the period after the sensitivity training session is less than the average number of complaints before the session. (Brase & Brase, Understandable Statistics, test item file p. 9-8)

One Sample Proportion z

A member of the House of Representatives wants to determine the proportion of voters in her district who favor a flat income tax. A random sample of 200 voters in her district showed 89 in favor. (Brase & Brase, Understandable Statistics, test item file p. 8-4)

a) Find a 95% confidence interval for the proportion of voters who favor a flat income tax.

b) Does the confidence interval indicate whether a majority of the voters oppose the tax? Explain.

A random sample of 400 families in the city of Minneapolis showed that 192 of them owned pets. The city council claims that 53% of the families in the city own pets. Does the data indicate that the actual percentage of families owning pets is less than the 53% claimed?

Two sample t

A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimates and ignore sampling error. An STS of 75 stores this month shows mean sales of 52 units of a small appliance, with standard deviation 13 units. During the same month last year, an SRS of 53 stores game mean sales of 49 units, with standard deviation 11 units. An increase from 49 to 52 is a rise of 6%. The marketing manager is happy because sales went up 6%. (Yates, Moore & McCabe, The Practice of Statistics, p. 641-642)

a) Find a 95% confidence interval for the difference between this year and last year in the mean number of units sold at all retail stores.

b) Should the manager be happy about this improvement? Explain using a significance test.

Two Sample Proportion z

Amos Tversky and Thomas Gilovich in their study on the “Hot Hand” in basketball (Chance, Winter 1989, p. 20), found that in a random sample of games, Larry Bird hit a second free throw in 48 of 53 attempts after the first free throw was missed, and hit a second free throw in 251 of 285 attempts after the first free throw was made. Is there sufficient evidence to say that the probability that Bird will make a second free throw is different depending on whether or not he made the first free throw?

A pollster wants to determine the difference between the proportions of high-income voters and low-income voters who support a decrease in the capital gains tax. If the answer must be known to within [pic]0.2 at the 95% confidence level and the sample sizes are identical, what samples should be taken?

Chi-Square Test for “Goodness of Fit”

In May 2002, the AP Statistics exam was administered to a total of 48,790 students. The grade distributions for these students were as follows:

Score: 5 4 3 2 1

Percent: 11.1 21.6 23.9 19.2 24.2

PWSH students taking the AP Statistics exam had the following distribution of grades:

Score: 5 4 3 2 1

Students: 16 21 11 2 0

Is the distribution of scores for PWSH students significantly different from the national distribution of scores?

Chi-Square Test for Homogeneity of Populations

Until recently a number of professions were prohibited from advertising. In 1977, the U.S. Supreme Court ruled that prohibiting doctors and lawyers fom advertising violated their right to free speech. The paper “Should Dentists Advertise?” (Journal of Advertising Research, June 1982) compared the attitudes of 101 consumers and 124 dentists to the questions “I favor the use of advertising by dentists to attract new patients”. Determine whether the two groups differed in their attitudes toward advertising. (handout from Michael Legacy)

| |Strongly | | | |Strongly |

|Group |Agree |Agree |Neutral |Disagree |Disagree |

|Consumers |34 |47 |9 |6 |5 |

|Dentists |9 |18 |23 |28 |46 |

Chi-Square Test for Independence

Highlands State College is doing a study to determine if fees for course schedule changes have any effect on the number of course schedule changes students make during the drop/add period. A random sample of student schedules showed the following data:

|Schedule |No fee |$25 fee |Row Total |

|No changes |125 |135 |260 |

|Changes |75 |65 |140 |

|Column Total |200 |200 |400 |

Use a 1% level of significance to test the claim that the number of course schedule changes is independent of the fee charged. (Brase & Brase, Understandable Statistics, test item file)

Linear Regression t

A teacher asked her eight introductory statistics students to record the total amount of time they spent studying for a particular test. The amounts of study time x (in hours) and the resulting test greased y are given below.

x 2 1 1.5 0.5 1 3 0 2

y 92 81 82 68 85 96 48 74

Suppose we want to find out if the number of hours studied helps predict the grade earned on this statistics test. Perform a significance test at the .05 significance level.

In-Class Problem

(from the 1998 AP Exam)

A large university provides enough housing for 10 percent of its graduate students to live on campus. The university office thinks that the percent of graduate students looking for housing on campus may be more than 10 percent. The housing office decides to survey a random sample of graduate students, and 62 of 481 respondents say that they are looking for housing on campus.

a) On the basis of the survey data, would you recommend that the housing office consider increasing the amount of housing on campus to graduate students? Give appropriate statistical ecidence to support your recommendation.

b) In addition to the 481 graduate students who responded to the survey, there were 19 who did not respond. If these 19 had responded, is it possible that your recommendation would have changed? Explain.

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