Question

Suppose that X1,...,Xn form a random sample from the normal distribution with unknown mean μ and known variance 1. Suppose also that μ0 is a certain specified number, and that the following hypotheses are to be tested: H0: μ = μ0, H1: μ = μ0. Finally, suppose that the sample size n is 25, and consider a test procedure such that H0 is to be rejected if |Xn − μ0| ≥ c. Determine the value of c such that the size of the test will be 0.05.

Answer 1

c=0.392

Explanation:

Given that X1,...,Xn form a random sample from the normal distribution with unknown mean μ and known variance 1.

Suppose also that μ0 is a certain specified number, and that the following hypotheses are to be tested:

`H0: \mu = \mu_0 Vs  H_1: \mu \\eq \mu_0`

This is two tailed test.

Alpha =0.05

Sample size = 25

we reject null hypothesis if
`\frac|{(1)/(√(25) ) } \geq 1.96`

Or
`|x_n - \mu_0|\geq 1.96/5 = 0.392`