Question

In 2000, in order to reduce the unemployment rate, France mandated all employers with 20 or more employees to reduce the workweek to 35 hours. Prior to the new law, the unemployment rate in France was 12%. In a random sample of 500 French workers taken a few years after the new law went into effect, 53 workers were found to be unemployed. Using the p-value method, conduct a hypothesis test to determine if the French unemployment rate dropped after the enactment of the 35- hour workweek law. Assume the significance level as 0.05. (7 Points)

Answer 1

We accept H₀ for a CI = 95 % we din´t find differences in the unemployment level

Explanation:

p₀ = 12 % p₀ = 0,12

From sample p = 53/500 p = 0,106

Test Hypothesis

Null Hypothesis H₀ p = p₀

Alternative Hypothesis Hₐ p < p₀

p₀*n = 0,12*500 = 60

q₀ * n = 0,88 * 500 = 440

Then the binomial distribution can be approximate to a normal distribution

The significance level α = 0,05 CI = 95 %

We need to develop a one-tail test (to the left ) find p-value and compare it with α.

p(s) = ( p - p₀ ) / √ p*q /n

p(s) = 0,106 - 0,12 / √(0,12)*(0,88)/500

p(s) = - 0,014 / 0,015

p(s) = - 0,93

With this P score we find the area under the bell shape curve

p-value = 0,1762 and compare that area with α = 0,05

Then p-value > 0,05

Therefore we accept H₀