Maxwell Cantor,VP of human resources of Asimov Aerospace Industries Inc.,is reviewing the technical certifications of employees in different divisions of the company.His goal is having 90% of technical employees with up-to-date certifications.The north-east division typically has maintained higher rates of up-to-date certifications than the southern division.He selects a random sample of 250 employees from the north-east division and 300 from the southern division and finds out that the number of employees with up-to-date certifications are 230 in the north-east division and 265 in the southern division.Assuming $\alpha$ = 0.01,the appropriate decision is ______. A) do not reject the null hypothesis $\mu$₁ − $\mu$₂ = 0 B) do not reject the null hypothesis p₁ − p₂ = 0 C) reject the null hypothesis $\mu$₁ − $\mu$₂ = 0 D) reject the null hypothesis p₁ − p₂ = 0 E) do not reject the null hypothesis p₁ − p₂ ≥ 0

Question

Quizplus · Accepted Answer

The appropriate statistical test for this scenario is a two-sample z-test for the difference in proportions. The null hypothesis is that there is no difference in the proportion of employees with up-to-date certifications between the north-east and southern divisions.

The test statistic can be calculated as:
z = (p1 - p2) / sqrt(p_hat * (1 - p_hat) * ((1/n1) + (1/n2)))
where p1 and p2 are the sample proportions, n1 and n2 are the sample sizes, and p_hat is the pooled proportion.

Plugging in the values given in the question, we get:
z = (0.92 - 0.883) / sqrt(0.896 * 0.104 * ((1/250) + (1/300)))
z = 2.26

Using a significance level of 0.01, the critical z-value is 2.33 (two-tailed test). Since our calculated z-value (2.26) is less than the critical z-value, we fail to reject the null hypothesis. Therefore, we conclude that there is not enough evidence to suggest that the proportion of employees with up-to-date certifications is significantly different between the north-east and southern divisions.

Hence, the correct choice is B, i.e., do not reject the null hypothesis p1 - p2 = 0.

Maxwell Cantor,VP of Human Resources of Asimov Aerospace Industries Inc α\alphaα

Maxwell Cantor,VP of Human Resources of Asimov Aerospace Industries Inc $\alpha$