Question

Show that the mean cost of all trips differs from 100.
After collecting a random sample of 13 trips
you find a sample mean of 81 and a sample standard
deviation of 19. Assume the distribution of cost is normal.
Test at a 1% significance level.

a. Determine the alternative hypothesis based on
what you wish to show.

b. Based on the alternative decide what
would cause you to reject the null and support
the alternative

c. Determine your critical value of the t and the rejection region

d. Calculate the test statistic using the formula:

e. Determine by your rule in c, if you should Reject Ho

f. Make a conclusion in context of the problem

*Please show the work and explain simply

Answer 1

a.Here claim is that the mean cost of all trips differs from 100.

So hypothesis is vs

b. As it is two tailed test, decision rule is Reject H0 if tstat<=-tcritical or tstat>=tcritical

c. The t-critical values for a two-tailed test, for a significance level of α=0.01 are

tc​=−3.055 and tc​=3.055

Graphically

d.

e. As tstatisitcs falls in the rejection region we reject the null hypothesis

f. We have sufficient evidence to support the claim that mean is different from 100