Question

A sample of 31 observations is selected from a normal population. The sample mean is 11, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.05 significance level. H0: μ ≤ 10 H1: μ > 10 Is this a one- or two-tailed test?

Answer 1

The test is a two -tailed test

Explanation:

From the question we are told that

The sample size is n = 31

The sample mean is
`\= x =11`

The sample standard deviation is
`\sigma = 3`

The null hypothesis is
`H_o: \mu \le 10`

The alternative hypothesis is
`H_1 : \mu > 10`

The level of significance is
`\alpha = 0.05`

The test statistics is mathematically represented as

`t = ( \= x - \mu )/( (\sigma )/(√(n) ) )`

substituting values

`t = ( 11 - 10 )/( (3)/(√( 31) ) )`

`t = 1.85`

The p- value is mathematically represented as

`p-value = p( t > 1.856) = 0.0317`

Looking at the value of
`p-value \ and \ \alpha` we see that
`p-value < \alpha` hence we reject the null hypothesis

Given the that the p value is less than 0.05 it mean the this is a two-tailed test