Answer to Question #250376 in Statistics and Probability for smilynne

Question

1. Explain the difference between testing a single mean and testing the difference between two means.

2. What two assumptions must be met when you are using the z test to test differences between two means? Can the sample standard deviations 𝑠1 and 𝑠2 be used in place of the population standard deviations 𝜎1 and 𝜎2? 

Answer 1

1.

for z- test:

testing a single mean:

$H_0:\mu=A$

$H_a:\mu\neq A$

$z=\frac{x-\mu}{\sigma}$

testing the difference between two means:

$H_0:\mu_1=\mu_2$

$H_a:\mu_1\neq \mu_2$

$z=\frac{\mu_1-\mu_2}{\sqrt{\sigma_1^2/n_1+\sigma^2_2/n_2}}$

2.

It can be:

$\sigma_1=\sigma_2$ or $\sigma_1\neq\sigma_2$

The sample standard deviations 𝑠1 and 𝑠2 cannot be used in place of the population standard deviations 𝜎1 and 𝜎2.

$s_1=\sigma_1/\sqrt{n_1}, s_2=\sigma_2/\sqrt{n_2}$