Question

Claim: The treatment and placebo groups have the same mean.

Treatment Group: sample size = 5, mean = 98.20, standard deviation = 0.62

Placebo Group: sample size = 25, mean = 104.60, standard deviation = 0.61

a) Assume equal variances to test this claim. Use a 0.05 level of significance.

b)Assume unequal variances to test this claim. Use a 0.05 level of significance.

Answer 1

Here we have following information:

a)

?Here hypotheses are:

Pooled standard deviation is :

and t-statistics will be

Here degree of feedom will be

Test is two tailed and df=28 so the p-value is:

p-value = 0.0000

Since p-value is less than 0.05 so we reject the null hypothesis.

b)

?Here hypotheses are:

Since it is given that variances are not equal so degree of freedom of the test is

So df is 5.

And test statistics will be

Test is two tailed and df=5 so the p-value is:

p-value = 0.0000

Since p-value is less than 0.05 so we reject the null hypothesis.