Question

1 - Acme claims that it takes a mean of 150 hours to produce a shipment of cartons. We want to collect enough data to show that the mean is actually more. In a sample of 300 shipments, the mean time to produce a shipment is 158 hours with a standard deviation of 60 hours.

(a) Determine the null and alternative hypotheses:

(b) Using α = 0.03, what is the rejection rule?

(c) Compute the test statistic.

(d) Should we reject H0?

(e) Based on your answer in part (d), what is your conclusion for THIS SITUATION? Be specific.

Answer 1

a)

H0: = 150

Ha: > 150

b)

t critical value at 0.03 significance level with 299 df = 1.888

Rejection rule = Reject H0 if t > 1.888

c)

Test statistics

t = ( - ) / ( S / sqrt(n) )

= ( 158 - 150) / ( 60 / sqrt(300) )

= 2.31

d)

Since test statistics value falls in rejection region, Reject H0.

e)

We have sufficient evidence to conlcude that the mean hours to produce a shipment of cartons

is actually more than 150 hours.