Question

A package delivery service advertises that 90% of all packages brought to its office by 9 am for delivery in the same city are delivered by noon that day. A new manager wants to improve that percentage. A month after extensive training of her personnel, she randomly selects 225 packages that arrived at the office by 9 am and finds out that 213 of those packages were actually delivered by noon the same day. Does she have enough evidence that the company have increased the percentage of package delivered by noon?

Answer 1

The null and alternate hypothesis are:

The test statistic value is given by:

Since this is a right tailed test, so the p-value is given by:

Let the level of signifiance be 0.05.

Since p-value is less than 0.05, so we have sufficient evidence to reject the null hypothesis H0 at 5% level of significance.

Thus we can conclude that the company has increased the percentage of package delivered by noon.