SOLUTION: A random selection of volunteers at a research institute have been exposed to a typical cold virus. After they started to have cold symptoms, 25 of them were given multivitamin tab

Question 1203279: A random selection of volunteers at a research institute have been exposed to a typical cold virus. After they started to have cold symptoms, 25 of them were given multivitamin tablets formulated to fight cold symptoms. The remaining 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.
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, u1, of the patients treated with multivitamin is not equal to the mean recovery time u2, of the patients who are treated with placebo tablets. At the 0.05 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. (If necessary, consult a list of formulas.)
Treated with multivitamin
7.3, 5.2, 2.6, 6.4, 7.3, 6.9, 3, 4.4, 8.2, 5.2
6.9, 2.3, 6.2, 2.6, 7.2, 7.2, 4.6
6.5, 6.7, 4.3, 8, 5.7, 4.5, 1.4, 4.6
_____________________________________________
Treated with Placebo
3.5, 5.3, 4.1
2.8, 2.9, 4.7
6.9, 3.9, 5, 4.8
5.5, 3.8

A.State the null hypothesis H0 and the alternative hypothesis
B.Determine the type of test statistic to use (Z, t, Chi-square, or F
C.Find the value of the test statistic to use. Round to 3 or more decimal places.
D.Find two critical values at the 0.05 level of significance. Round to 3 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 or no

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
use of the two sample z-test calculator at https://www.statskingdom.com/120MeanNormal2.html yields the following results.

the z-test was chosen because the population standard deviations were known and the test was for whether the means of the two samples were equal or not.

they would be considered equal if the results of the test was not significant.
the resutls of the test would not be considered significant if the two tailed p-vlue of the test was greater than .05.

the results of the test indicaed that the p-value of the test was greater than .05.
the results were therefore not considered significant and the decision was that there was not enough evidence to conswider the means of the two swamples to not be equal.
this means that the sample means were different due to normal variations in the mean of difference samples rather than any other reason for them to be different.

here are the results of the z-test.

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