Question

Assume the competing hypotheses take the following form: H0: µ1 – µ2 = 0, HA: µ1 – µ2 ≠ 0, where µ1 is the population mean for population 1 and µ2 is the population mean for population 2. Also assume that the populations are normally distributed and that the observations in the two samples are independent. The population variances are not known but are assumed equal. Which of the following expressions is appropriate test statistic?

a. taf
b. 2
c. 1-2 21 n
d. täf 2 t1

Answer 1

`t=\frac{\bar x_1- \bar x_2}{\sqrt{(s_1^2)/(n_1) +(s_2^2)/(n_2) } }`

Explanation:

H0: µ1 – µ2 = 0

HA: µ1 – µ2 ≠ 0

We have given,

The population variances are not known and cannot be assumed equal.

The test statistic for the test is

`t=\frac{\bar x_1- \bar x_2}{\sqrt{(s_1^2)/(n_1) +(s_2^2)/(n_2) } }`

Where,

`\bar x_1` = sample meaan of population 1

`\bar x_2` = sample mean of population 2

`n_1` = sample size of population 1

`n_2` = sample size of population 2

Therefore, this is the test

`t=\frac{\bar x_1- \bar x_2}{\sqrt{(s_1^2)/(n_1) +(s_2^2)/(n_2) } }`