Question

17.

Teacher salaries: A random sample of 50 public school teachers in Georgia had a mean annual salary of $48,300. Assume the population standard deviation is σ = $8,000. Can you conclude that the mean salary of public school teachers in Georgia differs from $50,000? Use the α = 0.01 level of significance.

Answer 1

H0: $\mu$ = 50000

Ha: $\mu$ $\neq$ 50000

Test statistics

z = ($\bar{x}$ - $\mu$ ) / ($\sigma$ / sqrt(n) )

= ( 48300 - 50000) / (8000 / sqrt(50) )

= -1.50

This is test statistics value.

Critical values at 0.01 level = -2.576 , 2.576

Since test statistics falls in non-rejection region, Do not reject H0.

We conclude at 0.01 level that we fail to support the claim.