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.

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.

Option A is correct

Step-by-step explanation:

From the question we are told that

     The  population mean is  $47,500

     The sample size is

      The sample  mean is  $48,061

      The standard deviation is $2,351

       The  level of significance is  

The null hypothesis  is  

     $47,500

 The  alternative hypothesis is

      $47,500

The critical value of   from the t-Distribution table is  

Now the test statistics is mathematically evaluated as

substituting values

Now from the values  obtained we can see that

hence we fail to reject the null hypothesis

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

a

step-by-step explanation: