Question

A recent report from the American Medical Association claims that for the first time in 10 years, the average salary of psychiatrists was $189,121 with a standard deviation of $26,975. A random sample of 64 psychiatrists this year yielded an average salary of $198,630. Is there evidence that the average salary is actually higher than what the American Medical Association reported

Answer 1

Answer:

Test statistic

        Z = 2.820 > 1.96 at 0.05 level of significance

Null hypothesis is rejected at 0.05 level of significance

The average salary is actually higher than the reported the average of American  Medical Association

Step-by-step explanation:

Step(i):-

Given data

sample size 'n' = 64

mean of the Population( μ)   =  $189,121

Standard deviation of the Population(σ) =  $26,975

Mean of the sample (x⁻) = $198,630

Step(ii):-

Null hypothesis : H₀ : there is no significance difference between the  means

Alternative Hypothesis :H₁ : The average salary is actually higher than the reported the average of American  Medical Association

Test statistic

               $Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }$

               $Z = \frac{198630 -189121}{\frac{26,975}{\sqrt{64} } }$

              Z =  2.820

Level of significance

∝ =0.05

$Z_{\alpha } = Z_{0.05} =1.96$        

Final answer:-

   Z = 2.820 > 1.96 at 0.05 level of significance

Null hypothesis is rejected at 0.05 level of significance

The average salary is actually higher than the reported the average of American  Medical Association