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A random selection of volunteers at a research institute have been exposed to a typical cold virus. After they started to have cold symptoms, 10 of them were given multivitamin tablets formulated to fight cold symptoms. The remaining 10 volunteers were given placebo tablets. For each individual, the length of time taken to recover from the cold is recorded. At the end of the experiment the following data are obtained. Days to recover from a cold Treated with multivitamin 2.6, 5.9, 5.3, 5.8, 8.7, 6.2, 7.6, 6.4, 8.0, 4.0 Treated with placebo 3.0, 5.1, 4.7, 4.2, 4.7, 5.6, 5.9, 4.7, 7.1, 4.9 It is known that the population standard deviation of recovery time from a cold is 1.8 days when treated with multivitamin tablets, and the population standard deviation of recovery time from a cold is 1.5 days when treated with placebo tablets. It is also known that both populations are approximately normally distributed. The researchers claim that the mean recovery time, Hz, of the patients treated with multivitamin is not equal to the mean recovery time H2, of the patients who are treated with placebo tablets. At the 0.01 level of significance, is there enough evidence to support this claim? Perform a two- tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (a) State the null hypothesis H, and the alternative hypothesis H1. Но (b) Determine the type of test statistic to use. •z • Chi-Square • F Degrees of freedom (if applicable): (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the two critical values at the 0.01 level of significance. (Round to three or more decimal places.) (e) Can we support the researchers' claim that the mean recovery time when treated with multivitamin is not equal to the mean recovery time when treated with placebo? Yes • No

A random selection of volunteers at a research institute have been exposed to a typical cold virus. After they started to have cold symptoms, 10 of them were given multivitamin tablets formulated to fight cold symptoms. The remaining 10 volunteers were given placebo tablets. For each individual, the length of time taken to recover from the cold is recorded. At the end of the experiment the following data are obtained. Days to recover from a cold Treated with multivitamin 2.6, 5.9, 5.3, 5.8, 8.7, 6.2, 7.6, 6.4, 8.0, 4.0 Treated with placebo 3.0, 5.1, 4.7, 4.2, 4.7, 5.6, 5.9, 4.7, 7.1, 4.9 It is known that the population standard deviation of recovery time from a cold is 1.8 days when treated with multivitamin tablets, and the population standard deviation of recovery time from a cold is 1.5 days when treated with placebo tablets. It is also known that both populations are approximately normally distributed. The researchers claim that the mean recovery time, Hz, of the patients treated with multivitamin is not equal to the mean recovery time H2, of the patients who are treated with placebo tablets. At the 0.01 level of significance, is there enough evidence to support this claim? Perform a two- tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (a) State the null hypothesis H, and the alternative hypothesis H1. Но (b) Determine the type of test statistic to use. •z • Chi-Square • F Degrees of freedom (if applicable): (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the two critical values at the 0.01 level of significance. (Round to three or more decimal places.) (e) Can we support the researchers' claim that the mean recovery time when treated with multivitamin is not equal to the mean recovery time when treated with placebo? Yes • No

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 random selection of volunteers at a research institute have been exposed to a typical cold virus. After they started to have cold symptoms, 10 of them were given multivitamin tablets formulated to fight cold symptoms. The remaining 10 volunteers were given placebo tablets. For each individual, the length of time taken to recover from the cold is recorded. At the end of the experiment the following data are obtained. Days to recover from a cold Treated with multivitamin 2.6, 5.9, 5.3, 5.8, 8.7, 6.2, 7.6, 6.4, 8.0, 4.0 Treated with placebo 3.0, 5.1, 4.7, 4.2, 4.7, 5.6, 5.9, 4.7, 7.1, 4.9 It is known that the population standard deviation of recovery time from a cold is 1.8 days when treated with multivitamin tablets, and the population standard deviation of recovery time from a cold is 1.5 days when treated with placebo tablets. It is also known that both populations are approximately normally distributed. The researchers claim that the mean recovery time, l, of the patients treated with multivitamin is not equal to the mean recovery time l, of the patients who are treated with placebo tablets. At the 0.01 level of significance, is there enough evidence to support this claim? Perform a two- tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (a) State the null hypothesis H, and the alternative hypothesis H. Но (b) Determine the type of test statistic to use. • Z • t • Chi-Square • F Degrees of freedom (if applicable): (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the two critical values at the 0.01 level of significance. (Round to three or more decimal places.) (e) Can we support the researchers' claim that the mean recovery time when treated with multivitamin is not equal to the mean recovery time when treated with placebo? • Yes • No
Transcribed Image Text:A random selection of volunteers at a research institute have been exposed to a typical cold virus. After they started to have cold symptoms, 10 of them were given multivitamin tablets formulated to fight cold symptoms. The remaining 10 volunteers were given placebo tablets. For each individual, the length of time taken to recover from the cold is recorded. At the end of the experiment the following data are obtained. Days to recover from a cold Treated with multivitamin 2.6, 5.9, 5.3, 5.8, 8.7, 6.2, 7.6, 6.4, 8.0, 4.0 Treated with placebo 3.0, 5.1, 4.7, 4.2, 4.7, 5.6, 5.9, 4.7, 7.1, 4.9 It is known that the population standard deviation of recovery time from a cold is 1.8 days when treated with multivitamin tablets, and the population standard deviation of recovery time from a cold is 1.5 days when treated with placebo tablets. It is also known that both populations are approximately normally distributed. The researchers claim that the mean recovery time, l, of the patients treated with multivitamin is not equal to the mean recovery time l, of the patients who are treated with placebo tablets. At the 0.01 level of significance, is there enough evidence to support this claim? Perform a two- tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (a) State the null hypothesis H, and the alternative hypothesis H. Но (b) Determine the type of test statistic to use. • Z • t • Chi-Square • F Degrees of freedom (if applicable): (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the two critical values at the 0.01 level of significance. (Round to three or more decimal places.) (e) Can we support the researchers' claim that the mean recovery time when treated with multivitamin is not equal to the mean recovery time when treated with placebo? • Yes • No
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