Question

An experiment was planned to compare the mean time (in days) required to recover from a common cold for persons given a daily dose of 4 milligrams (mg) of vitamin C, μ₂, versus those who were not, μ₁. Suppose that 32 adults were randomly selected for each treatment category and that the mean recovery times and standard deviations for the two groups were as follows.

Conduct the statistical test of the null hypothesis in part (a) and state your conclusion. Test using

α = 0.05.

(Round your answer to two decimal places.)

Find the test statistic.

z =

Find the rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)

z > z <

	No Vitamin Supplement	4 mg Vitamin C
Sample Size	32	32
Sample Mean	6.7	5.5
Sample Standard Deviation	2.7	1.3

Answer 1

the null and alternative hypothesis

Note : as we are to test whether there is a difference in recovery time (not specified whether one is less than other) we run two tailed test , thus alternative hypothesis is

Test statistic is

As population standard deviations are not known ,we replace them by sample standard deviations s1 and s2

Thus we get

For , two tailed critical value of z is

zc = 1.96

The rejection region is ( for two tailed test)

z > 1.96 , z < -1.96

Since calculated z > 1.96 ( that is in rejection region)

We reject H0

There is sufficient evidence to conclude that there is significant difference in average recovery time between those who took vitamin C and those who not .