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:
H0: μ1 - μ2 = 0Ha: μ1 - μ2 ≠ 0
Calculate Standard Error (SE):
SE = √s12/n1 + s22/n2SE = √52/100 + 52/100
SE = √25/100 + 25/100
SE = √0.25 + 0.25
SE = √0.5
SE = 0.70710678118655
Calculate Test Statistic:
| t = | X1 - X2 |
| SE |
| t = | 70 - 65 |
| 0.70710678118655 |
| t = | 5 |
| 0.70710678118655 |
t = 7.0710678118655
Calculate degrees of freedom:
| DF = | (s12/n1 + s22/n2)2 |
| (s12/n1)2/(n1 - 1) + (s22/n2)2/(n2 - 1) |
| DF = | (52/100 + 52/100)2 |
| (52/100)2/(100 - 1) + (52/100)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
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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) - zscoreα x √a < μ1 - μ2 < (x1 - x2) + zscoreα 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.
H1 - 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.
H0 - standard error
- measures how far the sample mean (average) of the data is likely to be from the true population mean
SE = σ/√n
