Question

The Municipal Transit Authority claims that, on weekdays, fewer passengers ride the train that departs at 8 a.m. than the one that departs at 2 p.m. The following sample statistics were determined. The table shows the average number of riders for each train, after samples from random days were taken for each train.

                                                n x bar s

            Morning Train             30                    323                  41

            Afternoon Train          45                    356                  45

            Test at the a=.05 level of significance whether the data provide sufficient evidence to conclude that fewer passengers ride the morning.

            a. State the Null and the Alternative Hypotheses, explaining which is mean 1 and which is mean 2. (2)

            c. State the conclusion about the claim and how you made the decision. (4)

Answer 1

We have given

	n	xbar	s
Morning Train	30	323	41
Afternoon Train	45	356	45

=.05

Null and the Alternative Hypotheses

Null Hypotheses:there is a no significant difference between population means of riders for each train,

Alternative Hypotheses: there is a significant difference between population means of riders for each train,

H0:μ1 = μ2

Ha: μ1 < μ2

Mean1=average number of riders for Morning train

Mean2=average number of riders for Afternoon train

Here we use two sample t-test

Hypothesis test

Formula:

=(323-356)/sqrt((41^2/30)+(45^2/45))

=-3.2831

Critical value of t at  =.05 significance level for n1+n2-2=30+45-2=73 degrees of freedom is

t0.05,73=-1.666(left tailed)

c) since calculated |t| is grreater than |t_critical|

|-3.2831|=3.2831 > |-1.666|=1.666

i.e Hence we reject H0

Conclusion:

data provide sufficient evidence to conclude that fewer passengers ride the morning.