Question 177525
H0 = 95% of orders filled
Ha = greater than 95% of orders filled

We'll use a z test for a proportion. The critical value for a one tailed alpha 0.025 test is z = 1.96. We'll reject the null hypothesis if our z test statistic is greater than that.

Find the test statistic z:

phat = 485/500 = 0.97

z = (phat-p)/sqrt(p*(1-p)/N)

z = (0.97-0.95)/sqrt(0.95*0.05/500)

z = 2.0519



This is greater than the z value from the table for a one tailed test, with alpha = 0.025 (z = 1.96), so we reject the null hypothesis. We can be reasonably sure that they are exceeding their goal.