Maureen McIlvoy,owner and CEO of a mail order business for wind surfing equipment and supplies,is reviewing the order filling operations at her warehouses. Her goal is 100% of orders shipped within 24 hours. In previous years,neither warehouse has achieved the goal,but the East Coast Warehouse has consistently out-performed the West Coast Warehouse. Her staff randomly selected 200 orders from the West Coast Warehouse (population 1)and 400 orders from the East Coast Warehouse (population 2),and reports that 190 of the West Coast Orders were shipped within 24 hours,and the East Coast Warehouse shipped 356 orders within 24 hours. Assuming $\alpha$= 0.05,the observed z value is ___________________.
A) -3.15
B) 2.42
C) 1.53
D) 0.95
E) 1.05

Question

Quizplus · Accepted Answer

We need to use the formula for the test statistic z:
z = (p1 - p2)/ sqrt(p_hat(1 - p_hat) * (1/n1 + 1/n2))
where 
p1 = proportion of orders shipped within 24 hours for West Coast Warehouse
p2 = proportion of orders shipped within 24 hours for East Coast Warehouse
p_hat = pooled proportion [(x1 + x2)/(n1 + n2)] where x1 is the number of successes in sample 1, x2 is the number of successes in sample 2, n1 is the sample size of sample 1, and n2 is the sample size of sample 2.

Plugging in the values:
p1 = 190/200 = 0.95
p2 = 356/400 = 0.89
p_hat = (190 + 356)/(200 + 400) = 0.906
n1 = 200
n2 = 400

z = (0.95 - 0.89) / sqrt(0.906*(1-0.906)*(1/200 + 1/400)) = 2.42 (rounded to two decimal places)

Since the calculated z value (2.42) is greater than the critical value of z (1.96), we reject the null hypothesis and conclude that there is a significant difference in the proportion of orders shipped within 24 hours between the West Coast Warehouse and the East Coast Warehouse.

Maureen McIlvoy,owner and CEO of a Mail Order Business for Wind