Question

A mail-order company that deals in small gifts charge a flat rate for postage, regardless of the weight of the package. The policy is based on the results of a study conducted several years ago that revealed the mean weight of mailed packages was 17.5 ounces. The accounting department feels that the mean weight of packages has increased and the company needs to increase the rate that is charged per package.   A sample of 75 packages was taken and the sample means weight was 18.4 ounces with a standard deviation of 3.6.

Do the sample results indicate that the mean weight of packages has increased?

Perform the appropriate hypothesis test using a significance level of 0.05

Show all the steps.

Do your work in an Excel file. Make Excel do the test statistic calculation.

Answer 1

Sol:

Ho:

Ha:

alpha=0.05

test statistic

t=xbar-mu/s/sqrt(n)

t=(18.4-17.5)/(3.6/sqrt(75))

t=2.165064

degrees of freedom=n-1=75-1=74

P value in excel for two tail t test for the t statistic,t=2.165064 and df=74 is

=T.DIST.2T(2.165064,74)

=0.033607212

p=0.0336

p<alpha

Reject null hypothesis

Acept alternative hypothesis

Conclusion:

There is suffcient statistical evidence at 5% level of significance to conclude that  the mean weight of packages has increased.