Question

Suppose that x is a normally distributed variable with variance 4. You collect a sample of size 100 for which you get a sample average value of ?̅. You are asked to test the null hypothesis that the mean is smaller than 2. Find the threshold for the average sample above which you can reject the null hypothesis with a 95% of confidence.

Answer 1

Here variance = = 4

sample size n = 100

here as hypothesis are

H₀ : = 2

H_a : < 2

here as we get the sample average value of ?̅

confidence level = 95%

critical test statistic = 1.96

standard error of mean = sqrt[/n]= sqrt [4/100] = 0.2

so here we will reject the null hypothesis if ?̅ < 2.0 - 1.96 * 0.2

?̅ < 1.608

so if we get the sample mean of size 100, sample mean should be less than 1.608 , that is the threshold.