# Example Paired t-Test for d̄ = 15, s = 7.5 & n = 27 at α = 0.5

Paired t-test solved example work with steps & calculation summary to estimate the t-statistic (t0), critical value (te) & hypothesis test (H0) for two small related samples with mean of related sample difference d̄ = 15, standard deviation s = 7.5 & sample size n = 27 at significance level α = 0.5.

Calculation Summary
mean of related sample difference (d̄)15
Standard deviation (s)7.5
Sample size (n)27
Significance Level (α)0.5
t010.3923
te0.68

## Work with Steps for d̄ = 15, s = 7.5 & n = 27

The paired t-test work with steps for mean of related sample difference (d̄) = 15, standard deviation (s) = 7.5 and sample size (n) = 27 to estimate the level of significance at α = 0.5 may helpful for beginners or grade school students to learn or solve similar practice or worksheet problems.
Workout :
step 1 Address the formula input parameters and values
mean of related sample difference (d̄) = 15
standard deviation (s) = 7.5
sample size (n) = 27
significance level (α) = 0.5

step 2 substitute the above input values in the formula.

t0=s/n

=15(7.5 / 27)

step 3 To find t0, simplify the above expression

=15 x 5.19627.5

=77.94237.5

t0 =10.3923

step 4 find expected or critical value te from the student's two tailed t-distribution table at the significance level α = 0.5 for degrees of freedom ν = n - 1 = 26

t e = 0.68

Inference
t0 > te
The null hypothesis H0 is rejected since t0 = 10.3923 is greater than the critical value for degrees of freedom te(25) = 0.68. Therefore, there is significant difference between the sample & population means.