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 some concern that it may be a health hazard. Radon detectors are sold to homeowners worried about their risk, but the detectors are sold to homeowners worried about their risk, but the detectors may be inaccurate. University researches placed 12 detectors in a chamber where they 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 96.6 119.4 104.8 101.7 Assume (unrealistically) that you know that the standard deviation of readings for all detectors of this type is =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.
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 some concern that it may be a health hazard. Radon detectors are sold to homeowners worried about their risk, but the detectors are sold to homeowners worried about their risk, but the detectors may be inaccurate. University researches placed 12 detectors in a chamber where they exposed to 105 Pico curies per liter of radon over 3 days. Here are the readings given by the detectors: 91.997.8111.4122.3105.495.0 103.899.696.6119.4104.8101.7 Assume (unrealistically) that you know that the standard deviation of readings for all detectors of this type is =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. Assumptions: · Have an SRS of detectors reading of radon per liter · The distribution is approximately normal · known · 90% confidence 100.782 We are 90% confident that the true mean of tightly closed houses and the readings of the detectors lie within 100.785 Pico curies per liter of radon and 107.483 Pico curies per liter of radon b) Is there significant evidence at the 10% level that the mean readings differ from the true value of 105? 101.016 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 a standard deviation of 0.6 pounds. a) Find a 90% confidence interval for the population mean weight of the fall lobsters. Assumptions: · Have an SRS of lobster’s weight · The distribution is approximately normal · unknown · 90% confidence (2.729-3.070) We are 90% confident that the true mean of the mean weight for the fall lobster lies within 2.729 pounds and 3.070 pounds. b) How many more lobsters should be included in the sample of we want to say with 90% confidence that the population mean weight of the fall lobsters catch is between 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 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. Auditor12345678910 Before 57238964103 After 7832577594 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. ONE SAMPLE PROPORTION z A member of the House of Representatives wants to determine the proportion of voters in her district who favor s flat income tax. A random sample of 200 voters in her district showed 89 in favor. 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 owned pets. Does the data indicate that the actual percentage of families owning pets is less that the 53% claimed? TWO SAMPLES PROPORTION t A market research firm supplies manufactures 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 a standard deviation of 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 t 52 is a rise of 6%. The marketing manager is happy because sales went up 6%. 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 found that in a random sample of games, Larry Bird hit a second free throw on 48 of 53 attempts after the first free throw was missed, and hit a second free thrown 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 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 ±.02 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:54321 Percent:11.121.623.919.224.2 PWSH students taking the AP Statistics exam had the following distributions of grades: Score:54321 Percent:16211120 Is the distribution of scores for PWSH students significantly different from the national distribution of scores? CHI-SQUARE TEST FOR HOMOGEINIY 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 from advertising violated their right to free speech. The paper “Should Dentist Advertise?” 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 towards advertising. Group Strongly Agree Agree Neutral Disagree Strongly disagree Consumers 34 47 9 6 5 Dentists 9 18 23 28 46 CHI-SQUARE TEST FOR INDEPENDCE 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 drop/add period. A random sample of students’ 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 change is independent of the fee charged 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. x211.50.51302 y9281826885964874 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 .05 significance level.