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A pharmaceutical company sells a tablet for treating colds. After extensive experimentation, researchers at the pharmaceutical company have developed a new formula for the tablet. The researchers suspect that the mean recovery time of all patients treated with the old tablet is more than the mean recovery time of all patients who are treated with the new tablet. To see if this is true, a random selection of volunteers were exposed to a typical cold virus. After they started to have cold symptoms, 20 of them were given the old tablet. The remaining 20 volunteers were given the new tablet. For each individual, the length of time taken to recover from the cold was recorded. At the end of the experiment the following data were obtained. Days to recover from a cold 3.7, 7.4, 5.8, 8.5, 4.0, 5.1, 4.6, 6.6, 4.5, 6.2, 4.4, 5.4, 5.1, 6.3, 9.4, 7.6, 6.4, 6.6, 6.9, 3.2 Treated with old tablet Treated with new tablet 4.0, 6.1, 3.8, 4.0, 5.5, 4.0, 5.4, 3.5, 4.4, 6.3, 4.4, 3.1, 3.9, 5.0, 5.2, 6.9, 5.5, 5.6, 6.0, 5.2 Send data to calculator V Send data to Excel It is known that the population standard deviation of the recovery time from a cold is 1.8 days when treated with the old tablet, and the population. standard deviation of the recovery time from a cold is 1.5 days when treated with the new tablet. It is also known that both populations are approximately normally distributed. At the 0.01 level of significance, is there enough evidence to support the claim that the mean recovery time, μ₁, of all patients treated with the old tablet is more than the mean recovery time, H₂, of all patients treated with the new tablet? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H₁. H:0 H₁ :0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) (e) Can we support the researchers' claim that the mean recovery time when treated with the old tablet is more than the mean recovery time when treated with the new tablet? Yes No Н X 0° a X S 2 P P 00 ローロ OSO 020 < >0

A pharmaceutical company sells a tablet for treating colds. After extensive experimentation, researchers at the pharmaceutical company have developed a new formula for the tablet. The researchers suspect that the mean recovery time of all patients treated with the old tablet is more than the mean recovery time of all patients who are treated with the new tablet. To see if this is true, a random selection of volunteers were exposed to a typical cold virus. After they started to have cold symptoms, 20 of them were given the old tablet. The remaining 20 volunteers were given the new tablet. For each individual, the length of time taken to recover from the cold was recorded. At the end of the experiment the following data were obtained. Days to recover from a cold 3.7, 7.4, 5.8, 8.5, 4.0, 5.1, 4.6, 6.6, 4.5, 6.2, 4.4, 5.4, 5.1, 6.3, 9.4, 7.6, 6.4, 6.6, 6.9, 3.2 Treated with old tablet Treated with new tablet 4.0, 6.1, 3.8, 4.0, 5.5, 4.0, 5.4, 3.5, 4.4, 6.3, 4.4, 3.1, 3.9, 5.0, 5.2, 6.9, 5.5, 5.6, 6.0, 5.2 Send data to calculator V Send data to Excel It is known that the population standard deviation of the recovery time from a cold is 1.8 days when treated with the old tablet, and the population. standard deviation of the recovery time from a cold is 1.5 days when treated with the new tablet. It is also known that both populations are approximately normally distributed. At the 0.01 level of significance, is there enough evidence to support the claim that the mean recovery time, μ₁, of all patients treated with the old tablet is more than the mean recovery time, H₂, of all patients treated with the new tablet? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H₁. H:0 H₁ :0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) (e) Can we support the researchers' claim that the mean recovery time when treated with the old tablet is more than the mean recovery time when treated with the new tablet? Yes No Н X 0° a X S 2 P P 00 ローロ OSO 020 < >0

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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A pharmaceutical company sells a tablet for treating colds. After extensive experimentation, researchers at the pharmaceutical company have developed a new formula for the tablet. The researchers suspect that the mean recovery time of all patients treated with the old tablet is more than the mean recovery time of all patients who are treated with the new tablet. To see if this is true, a random selection of volunteers were exposed to a typical cold virus. After they started to have cold symptoms, 20 of them were given the old tablet. The remaining 20 volunteers were given the new tablet. For each individual, the length of time taken to recover from the cold was recorded. At the end of the experiment the following data were obtained. Treated with old tablet Treated with new tablet Days to recover from a cold 3.7, 7.4, 5.8, 8.5, 4.0, 5.1, 4.6, 6.6, 4.5, 6.2, 4.4, 5.4, 5.1, 6.3, 9.4, 7.6, 6.4, 6.6, 6.9, 3.2 4.0, 6.1, 3.8, 4.0, 5.5, 4.0, 5.4, 3.5, 4.4, 6.3, 4.4, 3.1, 3.9, 5.0, 5.2, 6.9, 5.5, 5.6, 6.0, 5.2 Send data to calculator V Send data to Excel It is known that the population standard deviation of the recovery time from a cold is 1.8 days when treated with the old tablet, and the population standard deviation of the recovery time from a cold is 1.5 days when treated with the new tablet. It is also known that both populations are approximately normally distributed. At the 0.01 level of significance, is there enough evidence to support the claim that the mean recovery time, μ₁, of all patients treated with the old tablet is more than the mean recovery time, μ₂, of all patients treated with the new tablet? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H₁. : Ho H₁:0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) 0 Yes No (e) Can we support the researchers' claim that the mean recovery time when treated with the old tablet is more than the mean recovery time when treated with the new tablet? μ |x X O=O O X S P 믐 00 OSO 020 ☐ ☐ ☐<0. 0>0 S
Transcribed Image Text:A pharmaceutical company sells a tablet for treating colds. After extensive experimentation, researchers at the pharmaceutical company have developed a new formula for the tablet. The researchers suspect that the mean recovery time of all patients treated with the old tablet is more than the mean recovery time of all patients who are treated with the new tablet. To see if this is true, a random selection of volunteers were exposed to a typical cold virus. After they started to have cold symptoms, 20 of them were given the old tablet. The remaining 20 volunteers were given the new tablet. For each individual, the length of time taken to recover from the cold was recorded. At the end of the experiment the following data were obtained. Treated with old tablet Treated with new tablet Days to recover from a cold 3.7, 7.4, 5.8, 8.5, 4.0, 5.1, 4.6, 6.6, 4.5, 6.2, 4.4, 5.4, 5.1, 6.3, 9.4, 7.6, 6.4, 6.6, 6.9, 3.2 4.0, 6.1, 3.8, 4.0, 5.5, 4.0, 5.4, 3.5, 4.4, 6.3, 4.4, 3.1, 3.9, 5.0, 5.2, 6.9, 5.5, 5.6, 6.0, 5.2 Send data to calculator V Send data to Excel It is known that the population standard deviation of the recovery time from a cold is 1.8 days when treated with the old tablet, and the population standard deviation of the recovery time from a cold is 1.5 days when treated with the new tablet. It is also known that both populations are approximately normally distributed. At the 0.01 level of significance, is there enough evidence to support the claim that the mean recovery time, μ₁, of all patients treated with the old tablet is more than the mean recovery time, μ₂, of all patients treated with the new tablet? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H₁. : Ho H₁:0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) 0 Yes No (e) Can we support the researchers' claim that the mean recovery time when treated with the old tablet is more than the mean recovery time when treated with the new tablet? μ |x X O=O O X S P 믐 00 OSO 020 ☐ ☐ ☐<0. 0>0 S
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