Question

A human resources representative claims that the proportion of employees earning more than $50,000 is less than 40%. To test this claim, a random sample of 700 employees is taken and 305 employees are determined to earn more than $50,000. The following is the setup for this hypothesis test: {H0:p=0.40Ha:p<0.40 Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places. Provide your answer below:

Answer 1

Answer:  z(p) = 1.9286 and we reject H₀

Step-by-step explanation:

1) According to problem ststement : We need to  solve  an Hypotesis test proportion so:

H₀    P₀ = 0,4              and    Hₐ  < 0,4   ( Alternative hipotesis)

From 700 employes 305 are determined to earn more than $ 50000

Proportion                    pₐ = 305/700 = 0,4357     pₐ  = 0,4357

proportions are p = 0.4  and q = 0,6

We will asume a confidence level of 95 % hence α=  1-0,95     α = 0,05

so from z table we find z(c) = 1,64

Therefore we must calculate our z(p) = ( pₐ-p₀) ÷√(p*q)/n

Calculating   z(p)  =  0,0357 /0,01851   ⇒  z(p) 1.9286

Our test is one of the form  Hₐ <  ; that means is a right tail test, and the value z(p) is bigger than our critical value (z(c) = 1.64) so we rejecte H₀