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Volunteers who had developed a cold within the previous 24 hours were randomized to take either zinc or placebo lozenges every 2 to 3 hours until their cold symptoms were gone. Twenty-five participants took zinc lozenges, and 23 participants took placebo lozenges. The mean overall duration of symptoms for the zinc lozenge group was x, = 4.4 days, and the standard deviation of overall duration of symptoms was 1.4 days. For the placebo group, the mean overall duration of symptoms was x, = 7.9 days, and the standard deviation was 1.6 days. (a) Calculate x, - x, difference in sample means and also compute the unpooled s.e.(x, - x,) standard error of the difference in means. (Round all answers to the nearest hundredth.) X2 - X1 s.e.(x2 - x,) = | days days (b) Compute a 95% confidence interval for the difference in mean days of overall symptoms for the placebo and zinc lozenge treatments. Use the unpooled standard error and use the smaller of n, - 1 and n, - 1 as a conservative estimate of degrees of freedom. (Round the answers to one decimal place.) to days (c) Complete the following sentence interpreting the interval which was obtained in part (b). With 95% confidence, we can say that in the population of cold sufferers represented by the sample, taking zinc lozenges would reduce the mean number of days of symptoms by somewhere between and days, compared with taking a placebo.

Volunteers who had developed a cold within the previous 24 hours were randomized to take either zinc or placebo lozenges every 2 to 3 hours until their cold symptoms were gone. Twenty-five participants took zinc lozenges, and 23 participants took placebo lozenges. The mean overall duration of symptoms for the zinc lozenge group was x, = 4.4 days, and the standard deviation of overall duration of symptoms was 1.4 days. For the placebo group, the mean overall duration of symptoms was x, = 7.9 days, and the standard deviation was 1.6 days. (a) Calculate x, - x, difference in sample means and also compute the unpooled s.e.(x, - x,) standard error of the difference in means. (Round all answers to the nearest hundredth.) X2 - X1 s.e.(x2 - x,) = | days days (b) Compute a 95% confidence interval for the difference in mean days of overall symptoms for the placebo and zinc lozenge treatments. Use the unpooled standard error and use the smaller of n, - 1 and n, - 1 as a conservative estimate of degrees of freedom. (Round the answers to one decimal place.) to days (c) Complete the following sentence interpreting the interval which was obtained in part (b). With 95% confidence, we can say that in the population of cold sufferers represented by the sample, taking zinc lozenges would reduce the mean number of days of symptoms by somewhere between and days, compared with taking a placebo.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Volunteers who had developed a cold within the previous 24 hours were randomized to take either zinc or placebo lozenges every 2 to 3 hours until their cold symptoms were gone. Twenty-five participants took zinc lozenges, and 23 participants took placebo lozenges. The mean overall duration of symptoms for the zinc lozenge group was x, = 4.4 days, and the standard deviation of overall duration of symptoms was 1.4 days. For the placebo group, the mean overall duration of symptoms was x, = 7.9 days, and the standard deviation was 1.6 days. (a) Calculate x, - x, difference in sample means and also compute the unpooled s.e.(x, - x,) standard error of the difference in means. (Round all answers to the nearest hundredth.) X2 - X1 s.e.(x2 - x,) = | days days (b) Compute a 95% confidence interval for the difference in mean days of overall symptoms for the placebo and zinc lozenge treatments. Use the unpooled standard error and use the smaller of n, - 1 and n, - 1 as a conservative estimate of degrees of freedom. (Round the answers to one decimal place.) to days (c) Complete the following sentence interpreting the interval which was obtained in part (b). With 95% confidence, we can say that in the population of cold sufferers represented by the sample, taking zinc lozenges would reduce the mean number of days of symptoms by somewhere between and days, compared with taking a placebo.
Transcribed Image Text:Volunteers who had developed a cold within the previous 24 hours were randomized to take either zinc or placebo lozenges every 2 to 3 hours until their cold symptoms were gone. Twenty-five participants took zinc lozenges, and 23 participants took placebo lozenges. The mean overall duration of symptoms for the zinc lozenge group was x, = 4.4 days, and the standard deviation of overall duration of symptoms was 1.4 days. For the placebo group, the mean overall duration of symptoms was x, = 7.9 days, and the standard deviation was 1.6 days. (a) Calculate x, - x, difference in sample means and also compute the unpooled s.e.(x, - x,) standard error of the difference in means. (Round all answers to the nearest hundredth.) X2 - X1 s.e.(x2 - x,) = | days days (b) Compute a 95% confidence interval for the difference in mean days of overall symptoms for the placebo and zinc lozenge treatments. Use the unpooled standard error and use the smaller of n, - 1 and n, - 1 as a conservative estimate of degrees of freedom. (Round the answers to one decimal place.) to days (c) Complete the following sentence interpreting the interval which was obtained in part (b). With 95% confidence, we can say that in the population of cold sufferers represented by the sample, taking zinc lozenges would reduce the mean number of days of symptoms by somewhere between and days, compared with taking a placebo.
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