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 |
| t0 | 10.3923 |
| te | 0.68 |
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=d̄s/√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.
