Question

A sample of 30 observations is selected from a normal population. The sample mean is 21, and the population standard deviation is 6. Conduct the following test of hypothesis using the 0.05 significance level. H0 : μ ≤ 20 H1 : μ > 20

Answer 1

We conclude that μ <= 20 after hypothesis testing.

Explanation:

We are given that sample of 30 observations is selected from a normal population.

Also, Sample mean, Xbar = 21 and Population Standard deviation,
`\sigma` = 6.

Null Hypothesis,
`H_0` : μ <=20

Alternate Hypothesis,
`H_1` : μ > 20

So, Test Statistics we will use here is ;

`(Xbar-\mu)/((\sigma)/(√(n) ) )` follows standard normal, N(0,1)

Test statistics =
`(21 - 20)/((6)/(√(30) ) )` = 0.913 .

Now at 5% level of significance z % table gives the critical value of 1.6449 and our test statistics is less than this as 1.6449 > 0.913. So,we have sufficient evidence to do not reject null hypothesis or accept
`H_0` as our test statistics does not falls in the rejection region because it is less than 1.6449.

Hence we conclude after testing that Population mean, μ<=20.