Question

Consider the following hypothesis statement using alphaequals0.05 and data from two independent samples. Assume the population variances are not equal and the populations are normally distributed. Complete parts a and b. Upper H 0 : mu 1 minus mu 2 equals 0 x overbar 1 equals 115.1 x overbar 2 equals 122.0 Upper H 1 : mu 1 minus mu 2 not equals 0 s 1 equals 25.6 s 2 equals 14.5 n 1 equals 15 n 2 equals 21 a. Calculate the appropriate test statistic and interpret the result.

Answer 1

We have to test the hypothesis that

The difference between two means are significant.

against

i.e. Null Hypothesis -

against

( Two-tailed test)

From the information

n₁= 15 , n₂ =21

Alpha= level of significance = 0.05

since sample are coming from normal population and population variances are not equal.

Under Ho the value of test statistic

Where r is adjusted degrees of freedom which is calculated by formula

r = 20.40

Take integral portion of r

Hence degrees of freedom = 20

The value of test statistic is

Since the test is two-tailed and value of test statistic is -0.9415

p-value is obtained by

By using R

> pvalue=2*pt(-0.9415,20)
> pvalue
[1] 0.3576828
p-value = 0.3577

Decision : Since p-value is greater than level of significance alpha, we failed to reject the null hypothesis Ho at 5% level of significance.

Conclusion : There is no sufficient evidence to claim that the two means are significantly different.