Answer to Question #261919 in Statistics and Probability for Marcus

Question

A chef at an amusement park feels that the amount of time that people spend waiting in line to get served is too long. To determine if a new waitng procedure is effective in reducing the wait time, she measures the amount of time (in minutes) people are waiting in line for seven days. 

                                 Mon         Tues        Wed         Thurs        Fri            Sat           Sun

                                    

Wait time before        12            26            20             38            57            82             57

Wait time after           11            28            19             36            59            75             55

Is the new waiting  procedure effective in reducing the wait time at the =0.05 level of significance?

1. State the hypothesis and identify the claim.
2. Find the critical value(s)
3. Compute the Test value
4. Make a decision on the null hypothesis
5. Make a decision on the claim

Answer 1

1.

Paired T-Test

$H_0:\mu_2<\mu_1$ , the new waiting procedure effective in reducing the wait time

$H_a:\mu_2\ge\mu_1$ , the new waiting procedure is not effective in reducing the wait time

$\mu_1$ - mean of previous wait time

$\mu_2$ - mean of new wait time

2.

$df=n-1=7-1=6$

the critical value:

$T_{crit}=2.447$

3.

Test value:

$t=\frac{\mu_2-\mu_1}{\sqrt{s_1^2/n+s_2^2/n}}$

$\mu_1=41.7,s^2_1=617.6$

$\mu_2=40.4,s^2_2=542.0$ ,

$t=\frac{40.4-41.7}{\sqrt{617.6^2/7+542^2/7}}=-0.004$

4.

Since $|t|<t_{crit}$, we accept the null hypothesis.

5.

The new waiting procedure effective in reducing the wait time at the =0.05 level of significance.