Identify the correct HYPOTHESIS used in 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.

We accept H₀

Step-by-step explanation:

Population mean  μ₀ = 47500

Population standard deviation unknown

Sample size    n = 86   degree of freedom  df = 86 - 1  df = 85

Sample mean    μ = 48061

Sample standard deviation 2,351

The claim implies a two tail test with t-studend distributon

Null  Hypothesis                 H₀               μ  =  μ₀

Alternative Hypothesis      Hₐ               μ  ≠  μ₀      

Confidence Interval  mean α = 0,02     and   α/2  =  0,01

With α/2 and df = 85, from t-table we find  t(c)  critical value

t(c) = 2,3710

We compute t(s) as

t(s)  =  ( μ - μ₀ ) / s /√n

t(s)  = ( 48061 - 47500 )/ 2351/√86

t(s)  = 561 * 9,273 / 2351

t(s) = 2,212

Now we compare t(s) and t(c)

t(s) < t(c)       2,212  < 2,371

Then we are in the acceptance region. We accept H₀