A random selection of volunteers at a research institute have been exposed to a typical cold virus After they started to have cold symptoms 10 of them were given multivitamin tablets formulated to fight cold symptoms The remaining 10 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 Days to recover from a cold Treated with multivitamin 2 6 5 9 5 3 5 8 8 7 6 2 7 6 6 4 8 0 4 0 3 0 5 1 4 7 4 2 4 7 5 6 5 9 4 7 7 1 4 9 Treated with placebo 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 of the patients treated with multivitamin is not equal to the mean recovery time of the patients who are treated with placebo tablets At the 0 01 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 a State the null hypothesis Ho and the alternative hypothesis H Ho H b Determine the type of test statistic to use Z t Chi Square F Degrees of freedom if applicable c Find the value of the test statistic Round to three or more decimal places d Find the two critical values at the 0 01 level of significance Round to three 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