# 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 |

t_{0} | 10.3923 |

t_{e} | 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.

t_{0}=d̄s/√n

=15(7.5 / √27)

step 3 To find t_{0}, simplify the above expression

=15 x 5.19627.5

=77.94237.5

t_{0} =10.3923

step 4 find expected or critical value t_{e} 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__

t_{0} > t_{e}

The null hypothesis H_{0} is rejected since t_{0} = 10.3923 is greater than the critical value for degrees of freedom t_{e}(25) = 0.68. Therefore, there is significant difference between the sample & population *means*.