Question

Identify the CONCLUSION of a hypothesis test of the following claim and sample data: Claim: "The average annual household income in Warren County is $47,500." A random sample of 86 households from this county is obtained, and they have an average annual income of $48,061 with a standard deviation of $2,351. Test the claim at the 0.02 significance level.

Answer 1

Complete Question

The options for the above question is

a There is not sufficient evidence to warrant rejection of the claim.

b There is sufficient evidence to warrant rejection of the claim.

c There is sufficient evidence to support the claim.

d There is not sufficient evidence to support the claim.

Answer:

Option A is correct

Explanation:

From the question we are told that

The population mean is
`\mu =`$47,500

The sample size is
`n = 86`

The sample mean is
`\= x =`$48,061

The standard deviation is
`\sigma =`$2,351

The level of significance is
`\alpha = 0.02`

The null hypothesis is

`H_o : \mu =`$47,500

The alternative hypothesis is

`H_a : \mu \\e` $47,500

The critical value of
`\alpha` from the t-Distribution table is
`Z_{(\alpha )/(2) } = 2.326`

Now the test statistics is mathematically evaluated as

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

substituting values

`t = (48061 - 47500 )/((2351)/(√(86) ) )`

`t = 2.21`

Now from the values obtained we can see that

`Z_{(\alpha )/(2) } > t`

hence we fail to reject the null hypothesis

Hence there is not sufficient evidence to warrant rejection of the claim