An industrial researcher is a consultant to a large chain of bookstores. Industr
ID: 3133116 • Letter: A
Question
An industrial researcher is a consultant to a large chain of bookstores. Industry reports show that for book stores in general, the average number of complaints received by management for a 1-month period at this time of year is 6.5 (the variance is not known). Seven of this chain's stores are randomly selected to keep records of complaints received over a 1-month period. The numbers of complaints are 4, 8, 9,0, 3,5, and 6. Does this chain get a different amount of complaints than book stores in general? (Use the.05 level). Use the five steps of hypothesis testing.Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: u = 6.5
Ha: u =/ 6.5
As we can see, this is a two tailed test.
Thus, getting the critical t,
df = n - 1 = 6
tcrit = +/- 2.446911851
Getting the test statistic, as
X = sample mean = 5
uo = hypothesized mean = 6.5
n = sample size = 7
s = standard deviation = 3.055050463
Thus, t = (X - uo) * sqrt(n) / s = -1.299038106
Also, the p value is
p = 0.241614266
As |t| < 2.447, and P > 0.05, we FAIL TO REJECT THE NULL HYPOTHESIS.
Hence, there is no significant evidence that this chain gets a different amount of complaints than book stores in general at 0.05 level. [CONCLUSION]