1. The standard deviation of the diameter at breast height, or DBH, of the slash pine tree is less than one inch. Identify the Type I error. (Points : 1) Fail to support the claim < 1 when < 1 is true. Support the claim < 1 when = 1 is true. Support the claim < 1 when = 1 is true. Fail to support the claim < 1 when < 1 is true. 2. Biologists are investigating if their efforts to prevent erosion on the bank of a stream have been statistically significant. For this stream, a narrow channel width is a good indicator that erosion is not occurring. Test the claim that the mean width of ten locations within the stream is greater than 3.7 meters. Assume that a simple random sample has been taken, the population standard deviation is not known, and the population is normally distributed. Use the following sample data: 3.3 3.3 3.5 4.9 3.5 4.1 4.1 5 7.3 6.2 What is the P-value associated with your test statistic? Report your answer with three decimals, e.g., .987 . (Points : 1) 3. Scientists, researching large woody debris (LWD), surveyed the number of LWD pieces from aerial photos taken annually for the past 35 years at two different sites. Over the 35 years of photos examined, the first site had a mean number of LWD pieces per hectare per year (LWD/ha/yr) of 3.7 pieces with a standard deviation of 1.9. The second site had a mean number of LWD/ha/yr of 4.3 with a standard deviation of 2.4. Assume a .05 significance level for testing the claim that the mean LWD/ha at the first site had less than the mean LWD/ha/yr at the second site. Also, assume the two samples are independent simple random samples selected from normally distributed populations, but do not assume that the population standard deviations are equal. Construct a 90% confidence interval for the difference between the two means. Give your answer with two decimals, e.g., (12.34,56.78) (Points : 0.5) 4. The paired data consist of the cost of regionally advertising (in thousands of dollars) a certain pharmaceutical drug and the number of new prescriptions written (in thousands). Cost Number 9 85 2 52 3 55 4 68 2 67 5 86 9 83 10 73 Find the value of the linear correlation coefficient r . Give your answer to three decimals, e.g., .987 . (Points : 0.5) 5. Use a .05 significance level and the observed frequencies of 70 Neonatal deaths to test the claim that number of neonatal deaths on each day of the week is equally likely. Mon 10 Tues 9 Wed 5 Thurs 8 Fri 15 Sat 12 Sun 11 Determine the value of the 2 test statistic. Give your answer to two decimals, e.g., 12.34 (Points : 0.5) 6. Using a .01 significance level, test the claim that the proportions of fear/do not fear responses are the same for male and female dental patients. Gender Fear Dentistry Do Not Fear Dentistry Male 48 21 Female 70 32 Do you reject the null hypothesis, at the .01 significance level? Enter Y for yes (reject), N for no (fail to reject). (Points : 0.5) 7. The table represents results from an experiment with patients afflicted in both eyes with glaucoma. Each patient was treated in one eye with laser surgery and in the other eye was treated with eye drops. Using a .05 significance level, apply McNemar's test to test the following claim: The proportion of patients with no improvement on the laser treated eye and an improvement on the drops treated eye is the same as the proportion of patients with an improvement on the laser treated eye and no improvement on the drops treated eye. Eye Drop Treatment Improvement No Improvement Laser Surgery Treatment Improvement No Improvement 15 50 10 25 Determine the value of the 2 test statistic. Give your answer to two decimals, e.g., 12.34 . (Points : 0.5) 8. For a study on Type 1 diabetes, medical graduate students subdivided the United States into four study regions (Northeast, Southeast, Southwest, and Northwest). The students randomly selected seven patients per region and recorded the number of times during a randomly selected month that each patient used insulin shots to regulate blood sugar levels. Use One-Way ANOVA at a .05 significance level to test the claim that the means from the different regions are not the same. Mean number of times patients used insulin shots to regulate blood sugar levels Northeast 4 3 3 4 3 2 5 Southeast 6 5 6 8 6 6 8 Southwest 4 5 6 6 7 5 4 Northwest 4 4 5 6 3 5 3 Do you reject the null hypothesis, at the .05 significance level? Enter Y for yes (reject), N for no (fail to reject). (Points : 0.5 9. The reason we cannot use multiple t-tests to claim that four populations have the same mean is that we increase the likelihood of a type I error. (Points : 1) True False 10.Use the following technology display from a Two-Way ANOVA to answer this question. Biologists studying habitat use in Lepidopteran moths measured the number of savannah moths found at three randomly selected prairie sites with two potential habitat interferences (expansion of row crops and grazing). Use a .05 significance level. Source Site Habitat Site*Habitat Df 2 1 2 SS .1905 304.0238 .1905 MS .0952 304.0238 .0952 F .0381 121.6095 .0381 P .9627 .0000 .9627 What is the value of the F test statistic for the site effect? (Points : 0.5) 1. The standard deviation of the diameter at breast height, or DBH, of the slash pine tree is less than one inch. Identify the Type I error. (Points : 1) Fail to support the claim < 1 when < 1 is true. Support the claim < 1 when = 1 is true. Support the claim < 1 when = 1 is true. Fail to support the claim < 1 when < 1 is true. 2. Biologists are investigating if their efforts to prevent erosion on the bank of a stream have been statistically significant. For this stream, a narrow channel width is a good indicator that erosion is not occurring. Test the claim that the mean width of ten locations within the stream is greater than 3.7 meters. Assume that a simple random sample has been taken, the population standard deviation is not known, and the population is normally distributed. Use the following sample data: 3.3 3.3 3.5 4.9 3.5 4.1 4.1 5 7.3 6.2 What is the P-value associated with your test statistic? Report your answer with three decimals, e.g., .987 . (Points : 1) 0.029 3. Scientists, researching large woody debris (LWD), surveyed the number of LWD pieces from aerial photos taken annually for the past 35 years at two different sites. Over the 35 years of photos examined, the first site had a mean number of LWD pieces per hectare per year (LWD/ha/yr) of 3.7 pieces with a standard deviation of 1.9. The second site had a mean number of LWD/ha/yr of 4.3 with a standard deviation of 2.4. Assume a .05 significance level for testing the claim that the mean LWD/ha at the first site had less than the mean LWD/ha/yr at the second site. Also, assume the two samples are independent simple random samples selected from normally distributed populations, but do not assume that the population standard deviations are equal. Construct a 90% confidence interval for the difference between the two means. Give your answer with two decimals, e.g., (12.34,56.78) (Points : 0.5) The estimated 90% CI is: 0.22 to 2.18 4. The paired data consist of the cost of regionally advertising (in thousands of dollars) a certain pharmaceutical drug and the number of new prescriptions written (in thousands). Cost Number 9 85 2 52 3 55 4 68 2 67 5 86 9 83 10 73 Find the value of the linear correlation coefficient r . Give your answer to three decimals, e.g., .987 .(Points : 0.5) R=0.708 5. Use a .05 significance level and the observed frequencies of 70 Neonatal deaths to test the claim that number of neonatal deaths on each day of the week is equally likely. Mon 10 Tues 9 Wed 5 Thurs 8 Fri 15 Sat 12 Sun 11 Determine the value of the 2 test statistic. Give your answer to two decimals, e.g., 12.34 (Points : 0.5) 2 =5.98 6. Using a .01 significance level, test the claim that the proportions of fear/do not fear responses are the same for male and female dental patients. Gender Fear Dentistry Do Not Fear Dentistry Male 48 21 Female 70 32 Do you reject the null hypothesis, at the .01 significance level? Enter Y for yes (reject), N for no (fail to reject). (Points : 0.5) N for no (fail to reject) 7. The table represents results from an experiment with patients afflicted in both eyes with glaucoma. Each patient was treated in one eye with laser surgery and in the other eye was treated with eye drops. Using a .05 significance level, apply McNemar's test to test the following claim: The proportion of patients with no improvement on the laser treated eye and an improvement on the drops treated eye is the same as the proportion of patients with an improvement on the laser treated eye and no improvement on the drops treated eye. Eye Drop Treatment Improvement No Improvement Laser Surgery Treatment Improvement No Improvement 15 50 10 25 Determine the value of the 2 test statistic. Give your answer to two decimals, e.g., 12.34 . (Points : 0.5) The chi-square statistic is 0.37 8. For a study on Type 1 diabetes, medical graduate students subdivided the United States into four study regions (Northeast, Southeast, Southwest, and Northwest). The students randomly selected seven patients per region and recorded the number of times during a randomly selected month that each patient used insulin shots to regulate blood sugar levels. Use One-Way ANOVA at a .05 significance level to test the claim that the means from the different regions are not the same. Mean number of times patients used insulin shots to regulate blood sugar levels Northeast 4 3 3 4 3 2 5 ANOVA Source of Variatio n Between Groups Within Groups Total SS Southeast 6 5 6 8 6 6 8 df Southwest 4 5 6 6 7 5 4 Northwest 4 4 5 6 3 5 3 MS F P-value F crit 9.939394 0.000191 3.008787 35.14286 3 11.71429 28.28571 24 1.178571 63.42857 27 Do you reject the null hypothesis, at the .05 significance level? Enter Y for yes (reject), N for no (fail to reject). (Points : 0.5 Y for yes (reject) 9. The reason we cannot use multiple t-tests to claim that four populations have the same mean is that we increase the likelihood of a type I error. (Points : 1) True False 10.Use the following technology display from a Two-Way ANOVA to answer this question. Biologists studying habitat use in Lepidopteran moths measured the number of savannah moths found at three randomly selected prairie sites with two potential habitat interferences (expansion of row crops and grazing). Use a .05 significance level. Source Site Habitat Site*Habitat Df 2 1 2 SS .1905 304.0238 .1905 MS .0952 304.0238 .0952 F .0381 121.6095 .0381 P .9627 .0000 .9627 What is the value of the F test statistic for the site effect? (Points : 0.5) 0.0381 1. The standard deviation of the diameter at breast height, or DBH, of the slash pine tree is less than one inch. Identify the Type I error. (Points : 1) Fail to support the claim < 1 when < 1 is true. Support the claim < 1 when = 1 is true. Support the claim < 1 when = 1 is true. Fail to support the claim < 1 when < 1 is true. 2. Biologists are investigating if their efforts to prevent erosion on the bank of a stream have been statistically significant. For this stream, a narrow channel width is a good indicator that erosion is not occurring. Test the claim that the mean width of ten locations within the stream is greater than 3.7 meters. Assume that a simple random sample has been taken, the population standard deviation is not known, and the population is normally distributed. Use the following sample data: 3.3 3.3 3.5 4.9 3.5 4.1 4.1 5 7.3 6.2 What is the P-value associated with your test statistic? Report your answer with three decimals, e.g., .987 . (Points : 1) 0.029 3. Scientists, researching large woody debris (LWD), surveyed the number of LWD pieces from aerial photos taken annually for the past 35 years at two different sites. Over the 35 years of photos examined, the first site had a mean number of LWD pieces per hectare per year (LWD/ha/yr) of 3.7 pieces with a standard deviation of 1.9. The second site had a mean number of LWD/ha/yr of 4.3 with a standard deviation of 2.4. Assume a .05 significance level for testing the claim that the mean LWD/ha at the first site had less than the mean LWD/ha/yr at the second site. Also, assume the two samples are independent simple random samples selected from normally distributed populations, but do not assume that the population standard deviations are equal. Construct a 90% confidence interval for the difference between the two means. Give your answer with two decimals, e.g., (12.34,56.78) (Points : 0.5) The estimated 90% CI is: 0.22 to 2.18 4. The paired data consist of the cost of regionally advertising (in thousands of dollars) a certain pharmaceutical drug and the number of new prescriptions written (in thousands). Cost Number 9 85 2 52 3 55 4 68 2 67 5 86 9 83 10 73 Find the value of the linear correlation coefficient r . Give your answer to three decimals, e.g., .987 .(Points : 0.5) R=0.708 5. Use a .05 significance level and the observed frequencies of 70 Neonatal deaths to test the claim that number of neonatal deaths on each day of the week is equally likely. Mon 10 Tues 9 Wed 5 Thurs 8 Fri 15 Sat 12 Sun 11 Determine the value of the 2 test statistic. Give your answer to two decimals, e.g., 12.34 (Points : 0.5) 2 =5.98 6. Using a .01 significance level, test the claim that the proportions of fear/do not fear responses are the same for male and female dental patients. Gender Fear Dentistry Do Not Fear Dentistry Male 48 21 Female 70 32 Do you reject the null hypothesis, at the .01 significance level? Enter Y for yes (reject), N for no (fail to reject). (Points : 0.5) N for no (fail to reject) 7. The table represents results from an experiment with patients afflicted in both eyes with glaucoma. Each patient was treated in one eye with laser surgery and in the other eye was treated with eye drops. Using a .05 significance level, apply McNemar's test to test the following claim: The proportion of patients with no improvement on the laser treated eye and an improvement on the drops treated eye is the same as the proportion of patients with an improvement on the laser treated eye and no improvement on the drops treated eye. Eye Drop Treatment Improvement No Improvement Laser Surgery Treatment Improvement No Improvement 15 50 10 25 Determine the value of the 2 test statistic. Give your answer to two decimals, e.g., 12.34 . (Points : 0.5) The chi-square statistic is 0.37 8. For a study on Type 1 diabetes, medical graduate students subdivided the United States into four study regions (Northeast, Southeast, Southwest, and Northwest). The students randomly selected seven patients per region and recorded the number of times during a randomly selected month that each patient used insulin shots to regulate blood sugar levels. Use One-Way ANOVA at a .05 significance level to test the claim that the means from the different regions are not the same. Mean number of times patients used insulin shots to regulate blood sugar levels Northeast 4 3 3 4 3 2 5 ANOVA Source of Variatio n Between Groups Within Groups Total SS Southeast 6 5 6 8 6 6 8 df Southwest 4 5 6 6 7 5 4 Northwest 4 4 5 6 3 5 3 MS F P-value F crit 9.939394 0.000191 3.008787 35.14286 3 11.71429 28.28571 24 1.178571 63.42857 27 Do you reject the null hypothesis, at the .05 significance level? Enter Y for yes (reject), N for no (fail to reject). (Points : 0.5 Y for yes (reject) 9. The reason we cannot use multiple t-tests to claim that four populations have the same mean is that we increase the likelihood of a type I error. (Points : 1) True False 10.Use the following technology display from a Two-Way ANOVA to answer this question. Biologists studying habitat use in Lepidopteran moths measured the number of savannah moths found at three randomly selected prairie sites with two potential habitat interferences (expansion of row crops and grazing). Use a .05 significance level. Source Site Habitat Site*Habitat Df 2 1 2 SS .1905 304.0238 .1905 MS .0952 304.0238 .0952 F .0381 121.6095 .0381 P .9627 .0000 .9627 What is the value of the F test statistic for the site effect? (Points : 0.5) 0.0381