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 34 adults were randomly selected for each treatment category and that the mean recovery times and standard deviations for the two groups were as follows.

no vitamin supplement 4 mg vitamin C
sample size 35 35
sample mean 6.9 5.8
sample standard deviation 2.9 1.2

(a) Suppose your research objective is to show that the use of vitamin C reduces the mean time required to recover from a common cold and its complications. Give the null and alternative hypothesis for the test. Is this a one to one or a two tailed test?
(b) Conduct the statistical test of the null hypothesis in part (a) and state your conclusion. Test using alpha= .05.