Question

t = -17.108, df = 52.748, p-value < 2.2e-16

alternative hypothesis: true difference in means is not equal to 095 percent confidence interval: -6.322688 -4.995573 sample estimates: mean of 1 1.76087 mean of 2 7.42000

a)What is the null hypothesis?

b)Is the t statistic significant?

How do you know?

c)Interpret the findings in narrative form

Answer 1

We have given output of the two sample t test :

t = -17.108 , df = 52.748, p-value < 2.2e-16

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval: - 6.322688 , - 4.995573

sample estimates:

mean of 1 = 1.76087

mean of 2 = 7.42000

## a)What is the null hypothesis?

Ho : μ1 = μ2

( There is no difference between population means )

and

alternative H1 : μ1 ≠ μ2

( There is difference between population means )

it is two tailed test

## b)Is the t statistic significant ? How do you know?

Answer :

Yes , the t statistics significant .

we can use here p value approach

Decision :

we reject Ho if p value is less than α value , here p value is less than α value we can reject Ho .

and we know that if reject Ho then result is significant .

Conclusion :

There is sufficient evidence to conclude that there is true mean difference between population means at given level of significance .

# We can also use confidence interval and can give result :

if confidence interval include null value then result is not significant , here 95% confidence interval not

include null value hence result is significant ,  

by using p value approach and confidence interval result is same .

## c)Interpret the findings in narrative form

Answer :

it is two sample t test , test for population means ,

use two tailed test , we have to check our claim ,

by using testing of hypothesis and confidence interval it is cleared that our claim satisfy .

there is true mean difference between population means at given level of significance .