Question

A group of researchers reviewed a random sample size of 1600 people from the work force in a city and found that 100 of them are unemployed. A survey conducted by the Department of National Statistics show that the national unemployment rate is 8%. Can we accept the claim that the urban unemployment rate below the national rate?

Answer 1

H₀: p = 0.08

H₁: p < 0.08

= 100/1600 = 0.0625

The test statistic is

  

P-value = P(Z < -2.58)

= 0.0049

For alpha = 0.05, since the P-value is less than the significance level (0.0049 < 0.05), so we should reject the null hypothesis.

At 0.05 significance level, there is sufficient evidence to support the claim that the urban unemployment rate is below the national rate .