A 7,000-seat theater is interested in determining whether there is a difference
ID: 3227054 • Letter: A
Question
A 7,000-seat theater is interested in determining whether there is a difference in attendance between shows on Tuesday evening and those on Wednesday evening. Two independent samples of 25 weeks are collected for Tuesday and Wednesday. The mean attendance on Tuesday evening is calculated as 5,500, while the mean attendance on Wednesday evening is calculated as 5,850. The known population standard deviation for attendance on Tuesday evening is 550 and the known population standard deviation for attendance on Wednesday evening is 445. What are the appropriate hypotheses to determine whether there is a difference in attendance for shows on Tuesday evening and Wednesday evening? Use Tuesday attendance as population 1 mean 1 and Wednesday attendance as population 2 mean 2, or D as the mean difference in matched-pairs sampling.
a) H0: µD 0, HA: µD <0
b) H0: µD = 0, HA: µD 0
c) H0: µ1 – µ2= 0, HA: µ1 – µ2 0
d) H0: µ1 – µ2 0, HA: µ1 – µ2< 0
Explanation / Answer
Null hypothesis: Ho:mu1=mu2
Alternative hypothesis :Ha: mu1 not equal to mu2
We can use hhere two sample z test to test or determine whether there is a difference in attendance for shows on Tuesday evening and Wednesday evening.
The test statistic is
Z=(xbar1-xbar2)/sqrt(s1^2/n1+s2^2/n2)
=(5500-5850)/sqrt(550^2/25+445^2/25)
=-2.47
The p-value=2*P(Z<-2.47) =0.0134
Since the p-value is less than 0.05, we reject Ho.
Answer: Conclude that the mean attendance differs since the p-value = 0.0134 < 0.05.
Hope this will be helpful.
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