Contents
How do you test the equality of variance of two normal populations?
An F-test (Snedecor and Cochran, 1983) is used to test if the variances of two populations are equal. This test can be a two-tailed test or a one-tailed test. The two-tailed version tests against the alternative that the variances are not equal.
How do you test a population mean from a normal distribution with known standard deviation?
Distribution for the test: The population standard deviations are known so the distribution is normal. Using Equation ???, the distribution is: Since μ1≤μ2 then μ1−μ2≤0 and the mean for the normal distribution is zero. Figure 10.3….10.3: Two Population Means with Known Standard Deviations.
| Engine | Sample Mean Number of RPM | Population Standard Deviation |
|---|---|---|
| 1 | 1,500 | 50 |
| 2 | 1,600 | 60 |
What test is used to compare two groups if the population standard deviation is unknown and the sample sizes are small?
The test comparing two independent population means with unknown and possibly unequal population standard deviations is called the Aspin-Welch t-test. The degrees of freedom formula was developed by Aspin-Welch.
Which of the following is the null hypothesis for a two sample t-test?
The default null hypothesis for a 2-sample t-test is that the two groups are equal. You can see in the equation that when the two groups are equal, the difference (and the entire ratio) also equals zero.
How to test if two populations are equal?
Purpose: Test if variances from two populations are equal . An F-test (Snedecor and Cochran, 1983) is used to test if the variances of two populations are equal. This test can be a two-tailed test or a one-tailed test. The two-tailed version tests against the alternative that the variances are not equal.
How to test for equality of two variances?
Test if variances from two populations are equal. An F-test (Snedecor and Cochran, 1983) is used to test if the variances of two populations are equal. This test can be a two-tailed test or a one-tailed test.
What is the significance of two population means?
Test at a 5% level of significance. This is a test of two independent groups, two population means. The population standard deviations are unknown, but the sum of the sample sizes is 30 + 30 = 60, which is greater than 30, so we can use the normal approximation to the Student’s-t distribution.
Which is the normal distribution for two populations?
The sampling distribution for the difference between the means is normal and both populations must be normal. The random variable is ¯¯¯¯¯X1 −¯¯¯¯¯X2 X ¯ 1 − X ¯ 2. The normal distribution has the following format: Normal distribution is: ¯¯¯¯¯X1 −¯¯¯¯¯X2 ∼ N [μ1 −μ2,√(σ1)2 n1 + (σ2)2 n2] X ¯ 1 − X ¯ 2 ∼ N [ μ 1 − μ 2, ( σ 1) 2 n 1 + ( σ 2) 2 n 2]