Question

3. The U.S. Department of Labor stated that the national unemployment rate was 4.9%. Of a sample of 90 people in one city, 5.2% were unemployed. Can the city conclude that their unemployment rate is the same as the national average?

Answer 1

H₀: P = 0.049

H₁: P 0.049

The test statistic z = ( - p)/sqrt(P(1 - P)/n)

= (0.052 - 0.049)/sqrt(0.049 * (1 - 0.049)/90) = 0.13

P-value = 2 * P(Z > 0.13)

= 2 * (1 - P(Z < 0.13))

= 2 * (1 - 0.5517)

= 2 * 0.4483 = 0.8966

At 5% significance level, since the p-value is greater than the significance level (0.8966 > 0.05), so we should not reject the null hypothesis.

Yes, the city can conclude that their unemployment rate is the same as the national average.