Question

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 α = 0.01, the appropriate decision is ______.

do not reject the null hypothesis μ1 − μ2 = 0

do not reject the null hypothesis p1 − p2 = 0

reject the null hypothesis μ1 − μ2 = 0

reject the null hypothesis p1 − p2 = 0

do not reject the null hypothesis p1 − p2 ≥ 0

Answer 1

Let , p1 be the proportion rate of up-to-date certifications for the North-east division and p2 b ethe proportion rate of up-to-date certifications for the southern division.

Given ; n1=250, n2=300 , X1=230 , X2=265

The estimates of the sample proportios are ,

The pooles estimate is ,

The null and alternative hypothesis is ,

The test is one-tailed test.

The test statistic is ,

The critical value is , ; From Z-table

Reject rue : Reject Ho , if

Decision : Here ,

Therefore , do not reject the null hypothesis