Question

Problem TWO:

The ticket manager for the Detroit Pistons believes that season ticket holders of private suites at The Palace of Auburn Hills will have to drive further next season when the Pistons play at the new Little Caesars’ Arena in downtown Detroit as compared to similar season ticket customers for the Detroit Red Wings who previously played at Joe Louis Arena.

He surveyed 100 suite holders group and then conducted a z-test for Two Independent Samples (Sec.8.1).

The data:

Group                                  Sample Size                      Mean                    Standard Deviation

Piston fans                        35                                          23.8 miles          6.4 miles

Red Wing fans                 65                                          19.7 miles          5.9 miles

a…..At α = 0.05, what is the Critical Value?

b…..What is the value of the Test Statistic?

c…..At α = 0.05, would you Reject the Null Hypothesis?......Yes or No??

d….What is the p-value for this study?                                                                                             

. ANSWERS

a)

b)

c)

                                                                                                                                 d)

Answer 1

(a)

= 0.05

One Tail - Right Side Test

From table, critical value of Z = 1.645

So,

Critical value = 1.645

(b)

Test statistic is:
Z = (23.8-19.7)/1.3061 = 3.1391

(c)

Since calculated value of Z= 3.1391 is greater than critical value of Z= 1.645, the difference is significant. Reject null hypothesis.

So,

Correct option:

Yes

(d)

Z score = 3.1391

From Table, area = 0.4992

So,

p - value= 0.05 - 0.4992 = 0.0008

So, answers are:

(a) 1.645

(b) 3.1391

(c) Yes

(d) 0.0008