A small sample of 100 units has a mean 70 and a standard deviation σ of 5Another 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 hypothesisopposite of null hypothesis. One of the proposed proposition in the hypothesis test.H1confidence intervala 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 meanshypothesis testingstatistical test using a statement of a possible explanation for some conclusionsmeanA statistical measurement also known as the averagenull hypothesisin a statistical test, the hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.
H0standard errormeasures 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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