Question

test the claim about the population mean μ at the given level of significance using the given sample statistics. Claim: μ ≠ 5000; α =0.06. Sample statistics: x= 5100, s = 343, n = 50 identify the null and alternative hypotheses.

Answer 1

Null hypothesis =
`H_0:\mu = 5000`

Alternate hypothesis=
`H_a:\mu \\eq 5000`

We accept the null hypothesis

Explanation:

Given : Claim: μ ≠ 5000; α =0.06. Sample statistics: x= 5100, s = 343, n = 50

To Find :test the claim about the population mean μ at the given level of significance using the given sample statistics. and identify the null and alternative hypotheses.

Solution:

Claim: μ ≠ 5000; α =0.06

So, Null hypothesis =
`H_0:\mu = 5000`

Alternate hypothesis=
`H_a:\mu \\eq 5000`

Sample statistics: x= 5100, s = 343, n = 50

Since n > 30

So, we will use z test

`z =(x-\mu)/((s)/(√(n)))`

Substitute the values

`z =(5100-5000)/((343)/(√(50)))`

`z =2.06`

refer the z value using z table

P(z) = 0.9803

So, p value is 0.9803

Since p value is greater than α

So, we accept the null hypothesis