A small sample of 100 units has a mean 70 and a standard deviation σ of 5

Another small sample of 100 related units has a mean 65 and a standard deviation σ of 5

Perform a hypothesis test with α = 99

## State Hypothesis:

H

_{0}: μ

_{1} - μ

_{2} = 0

H

_{a}: μ

_{1} - μ

_{2} ≠ 0

## Calculate Standard Error (SE):

SE = √

s_{1}^{2}/n_{1} + s_{2}^{2}/n_{2}SE = √

5^{2}/100 + 5^{2}/100SE = √

25/100 + 25/100SE = √

0.25 + 0.25SE = √

0.5SE = 0.70710678118655

## Calculate Test Statistic:

t = | 70 - 65 |

| 0.70710678118655 |

t = 7.0710678118655

## Calculate degrees of freedom:

DF = | (s_{1}^{2}/n_{1} + s_{2}^{2}/n_{2})^{2} |

| (s_{1}^{2}/n_{1})^{2}/(n_{1} - 1) + (s_{2}^{2}/n_{2})^{2}/(n_{2} - 1) |

DF = | (5^{2}/100 + 5^{2}/100)^{2} |

| (5^{2}/100)^{2}/(100 - 1) + (5^{2}/100)^{2}/(100 - 1) |

DF = | (25/100 + 25/100)^{2} |

| (25/100)^{2}/99 + (25/100)^{2}/99 |

DF = | (0.25 + 0.25)^{2} |

| (0.25)^{2}/99 + (0.25)^{2}/99 |

DF = | (0.5)^{2} |

| 0.0625/99 + 0.0625/99 |

DF = | 0.25 |

| 0.00063131313131313 + 0.00063131313131313 |

DF = | 0.25 |

| 0.0012626262626263 |

DF = 198, rounded to an integer is 198

##### What is the Answer?

DF = 198, rounded to an integer is 198

##### How does the Confidence Interval/Hypothesis Testing for the Difference of Means Calculator work?

Free Confidence Interval/Hypothesis Testing for the Difference of Means Calculator - Given two large or two small distriutions, this will determine a (90-99)% estimation of confidence interval for the difference of means for small or large sample populations.

Also performs hypothesis testing including standard error calculation.

This calculator has 7 inputs.

### What 2 formulas are used for the Confidence Interval/Hypothesis Testing for the Difference of Means Calculator?

α = 1 - Confidence%

(x1 - x2) - zscore

_{α} x √a < μ1 - μ2 < (x1 - x2) + zscore

_{α} x √a

For more math formulas, check out our

Formula Dossier
### What 7 concepts are covered in the Confidence Interval/Hypothesis Testing for the Difference of Means Calculator?

- alternative hypothesis
- opposite of null hypothesis. One of the proposed proposition in the hypothesis test.

H_{1} - confidence interval
- a range of values so defined that there is a specified probability that the value of a parameter lies within it.
- confidence interval/hypothesis testing for the difference of means
- hypothesis testing
- statistical test using a statement of a possible explanation for some conclusions
- mean
- A statistical measurement also known as the average
- null hypothesis
- in a statistical test, the hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.

H_{0} - standard error
- measures how far the sample mean (average) of the data is likely to be from the true population mean

SE = σ/√n

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