Question

Using R and R Commander, perform an Independent samples t-test on the variable attpublicschools selecting gender as grouping variable. Click on Options tab and select Yes under Assume equal variances? Copy the output and paste it below this question. Is the t-test significant at 5% alpha level? Can you explain it to me?

Here is my data:

Two Sample t-test

data: attpublicschools by gender
t = -0.29221, df = 22, p-value = 0.7729
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-1.496965 1.127217
sample estimates:
mean in group Female mean in group Male
5.529412 5.714286

Answer 1

We have given output of the two independent sample t test :

To test :

Ho : μ1 = μ2 vs H1: μ1 ≠ μ2

Where μ1 : population mean for male and μ2 : population mean for female

( it is two tailed test )

Test statistics : t

t = -0.29221,

df = 22 ( degree of freedom )

p-value = 0.7729

α = 95 % ie 0.05 ( level of significance )

Decision : We reject Ho if p value is less than α value using p value approach here p value is greater  than  α value we fail to reject Ho at given level of significance .

Conclusion : There is Insufficient evidence to conclude that  true difference in means is not equal to 0.

ie ( μ1  = μ2) that is result is Insignificant .  

### We have 95 percent confidence interval:

[-1.496965 , 1.127217 ]

We know that if confidence interval include null or zero value result is not significant or insignificant .

here in this confidence interval null value include hence we can say that result is not significant or insignificant at given level of significance . so we can say that ( μ1  = μ2)

## Result is  same from hypothesis testing and confidence interval :