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 remaining 15 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:

Treated with multivitamin

4.4, 5.6, 4.4, 4, 3, 5.8, 3.7, 7.2, 8.4, 4.6, 2.6, 4.4, 7, 3.9, 3.6

Treated with Vitamin C

2.6, 3.5, 3.9, 5.1, 2.4, 4.6, 3.4, 5.6, 6.4, 4.9, 4.2, 6.1, 1.2, 5.1, 3.4

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table.

The null hypothesis:

The alternative hypothesis:

The type of test statistic:

The value of the test statistic:

(Round to at least three decimal places.)

The p-value:

(Round to at least three decimal places.)

Can we reject the researchers' claim that the mean recovery time when treated with multivitamin is less than or equal to the mean recovery time when treated with vitamin C only?