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

Step-by-step 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

      $H_a : \mu \ne$ $47,500

The critical value of  $\alpha$ from the t-Distribution table is  $Z_{\frac{\alpha }{2} } = 2.326$

Now the test statistics is mathematically evaluated as

       $t = \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }$

substituting values

      $t = \frac{48061 - 47500 }{\frac{2351}{\sqrt{86} } }$

      $t = 2.21$

Now from the values  obtained we can see that

        $Z_{\frac{\alpha }{2} } > t$

hence we fail to reject the null hypothesis

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