Question

A web-based company has a goal of processing at least 95% of its orders on the same day they are received. If 390 out of the next 400 orders are processed on the same day, The sample data suggests that the web-based company might have met its goal, but is there strong enough evidence to state the company has met its goal?

a. Write appropriate alternative and null hypotheses to test that the company has met its goal.

b. Calculate the test statistic and p-value using Excel.

c. Using an α=0.05 significance level, make a statistical conclusion written in terms of the question statement.

d. Using an α=0.01 significance level, make a statistical conclusion written in terms of the question statement.

Answer 1

The null hypothesis (H0) is that the web-based company has not met its goal of processing at least 95% of its orders on the same day they are received. The alternative hypothesis (Ha) is that the company has met its goal. The p-value is used to determine if there is enough evidence to reject the null hypothesis and conclude that the company has met its goal.

Step-by-step explanation:

a. The null hypothesis (H0) is that the web-based company has not met its goal of processing at least 95% of its orders on the same day they are received. The alternative hypothesis (Ha) is that the company has met its goal.

b. To calculate the test statistic and p-value, we need to use the binomial distribution. The test statistic is the number of orders processed on the same day, which is 390. The p-value can be calculated using Excel's BINOM.DIST function.

c. Using an α=0.05 significance level, if the p-value is less than 0.05, we reject the null hypothesis and conclude that there is strong enough evidence to state that the company has met its goal. If the p-value is greater than or equal to 0.05, we fail to reject the null hypothesis and do not have enough evidence to conclude that the company has met its goal.

d. Using an α=0.01 significance level, the decision would be the same as in part c, but the threshold for rejecting the null hypothesis would be stricter. If the p-value is less than 0.01, we reject the null hypothesis and conclude that there is strong enough evidence to state that the company has met its goal.