Question

1. Stress and weight in rats. In a study of the effects of stress on weight in rats, 71 rats were randomly assigned to either a stressful environment or a control (nonstressful) environment. After 21 days, the change in weight (in grams) was determined for each rat. The table below summarizes the data on weight gain. Test the claim that stress effects weight. (Use a 10% significance level.)

Group	n	Sample mean	Sample Standard Dev.
Stress	20	26	13.4
No stress	51	32	14.2

Answer 1

GIVEN:

Sample size of group (Stress) 1

Sample size of group (No Stress) 2

Sample mean of group (Stress) 1

Sample mean of group (No Stress) 2

Sample standard deviation of group (Stress) 1

Sample standard deviation of group (No Stress) 2

I have used two independent sample t test with unequal variance to test the claim that stress effects weight. (That is, the average weight gain for stress group is more than the no stress group.)

HYPOTHESIS:

The hypothesis is given by,

(That is, the average weight gain for stress group is more than the average weight gain for the non stress group.)

(That is, the average weight gain for stress group is less than the average weight gain for the non stress group.)

LEVEL OF SIGNIFICANCE:

TEST STATISTIC:

which follows t distribution with degrees of freedom.

where the hypothesized value

CALCULATION:

  

  

CRITICAL VALUE:

The one tailed (since ) t critical value with degrees of freedom at significance level is .

DECISION RULE:

INFERENCE:

Since the t test statistic value (-1.39) is less than the t critical value (-1.294), we fail to reject null hypothesis and conclude that the average weight gain for stress group is more than the average weight gain for the non stress group. Thus the stress effects weight.