Answer to Question #261694 in Statistics and Probability for leveleu

Question

A quality-control manager at an amusement park feels that the amount of time that people spend waiting in line to ride the roller coaster is too long. To determine if a new loading and unloading procedure is effective in reducing the wait time, she measures the amount of time (in minutes) people are waiting in line for seven days. To make a reasonable comparison, she chooses times when whether conditions are similar.

        

                                                 Mon       Tues      Wed      Thurs       Fri         Sat          Sun

                                             2 p.m.    2 p.m.    2 p.m.    2 p.m.    2 p.m.    4 p.m.    12 noon

          Wait time before, 𝑋₁       12          26          20          38          57          82            57

          Wait time after, 𝑋₂          11          28          19          36          59          75            55

         

 

Is the new loading and unloading procedure effective in reducing the wait time at the α = 0.05 level of significance?

 

 

a.     State the hypothesis and identify the claim of the researcher.

b.     Find the critical value(s).

c.     Compute the test value.

d.     Make a decision on the null hypothesis. 

e.     Make a decision on the claim of the researcher. 

Answer 1

Paired sample T-test

a.

$H_0:\mu_1=\mu_2$ , new loading and unloading procedure is not effective in reducing the wait time (average amounts of wait time are equal)

$H_a:\mu_2<\mu_1$ , new loading and unloading procedure is effective in reducing the wait time (average amount of wait time "after" is less than average amount of wait time "before")

b.

$df=n-1=6$

critical value:

$t_{crit}=2.232$

c.

test value:

$t=\frac{\mu_2-\mu_1}{s_d/\sqrt n}=\frac{-1.29}{1.149/\sqrt 7}=-1.119$

where s_d is standard deviation of the difference

d.

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

e.

new loading and unloading procedure is not effective in reducing the wait time