Question

Test to determine if we can infer at the 5% significance level that the population mean is not equal to 20:

Answer 1

Here = 5% = 0.05

We want to test population mean is either equal or not equal to 20.

Then our hypotheses are

Ho : vs Ha :

Here our test statistic is

where M= sample mean

n = sample size

= population standard deviation

Now calculate critical value from z table

Critical value = = Z_{​​​​​​0.025 [ for both tailed test]}

Now reject Ho iff |Z|< Critical value at 5% level

That means if |Z| < critical Value then accept the fact that population mean is not equal to 20.