Question

A random selection of volunteers at a research institute have been exposed to a typical cold virus. After they started to have cold symptoms,

15

of them were given multivitamin tablets daily which contain

3

grams of vitamin C and various other vitamins and minerals. The remaining

15

volunteers were given placebo tablets. For each individual, the length of time taken to recover from cold is recorded. At the end of the experiment following data are obtained:

	Days to recover from cold
Treated with multivitamin	8.9, 6.2, 4.4, 6.4, 7.7, 2.6, 3.6, 5.5, 3.3, 6.3, 2.9, 4.9, 5.1, 2.2, 7.5
Treated with placebo	7.6, 5, 5.4, 5.6, 6.9, 3.5, 4.2, 5.3, 6, 6.3, 4.9, 3.1, 5, 4.7, 4.5

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It is known that the population standard deviation of recovery time from cold is

1.8

days when treated with multivitamin, and the population standard deviation of recovery time from 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,

μ1

, of the patients treated with multivitamin is not equal to the mean recovery time

μ2

, of the patients who are treated with placebo tablets. At the

0.1

level of significance, is there enough evidence to support this claim? Perform a two-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic: (Choose one)ZtChi squareF The value of the test statistic: (Round to at least three decimal places.) The two critical values at the 0.1 level of significance: (Round to at least three decimal places.) and 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

Answer 1

using excel>data>data analysis>two sample z we have

z-Test: Two Sample for Means
	treated with mutivitamin	placebo
Mean	5.166667	5.2
Known Variance	3.24	2.25
Observations	15	15
Hypothesized Mean Difference	0
z	-0.0551
P(Z<=z) one-tail	0.47803
z Critical one-tail	1.281552
P(Z<=z) two-tail	0.95606
z Critical two-tail	1.644854

The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic: Z The value of the test statistic: (Round to at least three decimal places.) -0.055 The two critical values at the 0.1 level of significance: (Round to at least three decimal places.) -1.645 and 1.645 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 because test statistic is in between -1.645 and 1.645