PLease show step and calculation formula that involed A plan

PLease show step and calculation (formula that involed)

A plant biologist studied whether physical stress can slow the growth of soybean plants. Prior to the study, a hypothesis was formulated, based on other plant species, that physical stress should make growth slower. Two groups of 13 plants were grown under identical conditions in a greenhouse. The treatment group was shaken by a mechanical device for 20 minutes twice every day (simulating stress caused by winds), while the control group was not shaken. After 16 days of growth, plant height in cm was measured, and the following data were obtained. Using the following summary data, do a hypothesis test with = 0.05 that addresses the plant biologist’s prior hypothesis, and state the conclusion of the test.

                            Control             Treatment

          n                      13                       13

Sample Mean                    30.59                  27.78

Sample SD           2.13                       1.73

Solution

Let mu1 be the mean for control group and mu2 treatment groups

H0: mu1 = mu2

Ha: mu1 > mu2

Right tailed test

As sample size <30, t test can be used.

  standard error of difference = 2.744

The mean of Group One minus Group Two equals 2.8100

t = 1.0240
  df = 24

The two-tailed P value equals 0.3160
  By conventional criteria, this difference is considered to be not statistically significant.

Hence at 0.05 level there is no evidence to support biologist claim