Hypothesis test for the difference of population means: Z test

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 1 gram of vitamin C and various other vitamins and minerals. The remaining15 volunteers were given tablets only containing 4 grams of vitamin C. For each individual, the length of time taken to recover from cold is recorded. At the end of the experiment the following data are obtained:

Days to recover from cold Treated with multivitamin3.9, 6.4, 2.6, 4.5, 6.1, 8.0, 5.8, 3.4, 3.6, 7.8, 5.6, 4.4, 6.2, 5.7, 5.4

Treated with Vitamin C5.5, 5.3, 5.4, 3.7, 4.4, 2.6, 2.6, 2.8, 3.5, 6.0, 3.9, 3.8, 5.0, 4.3, 3.4

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 vitamin C 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 less than or equal to the mean recovery time , of the patients who are treated with vitamin C tablets. At the 0.01 level of significance, is there enough evidence to reject this claim? Perform a one-tailed test. Then fill in the table below.

1) The Null Hypothesis:H0

2) The alternative Hypothesis:H1

3) The type of test statistic:

4) The value of the test statistic:

5) The critical value at the 0.01 level of significance:

6) Canwe reject the researchers claim that the mean recovery time when treated with multivitamin is less the or equal to the mean recovery time whentreated with vitamin C only?Yes or NO?