The corporate management at a paper company has reason to believe one of its (su
ID: 3217393 • Letter: T
Question
The corporate management at a paper company has reason to believe one of its (supposed) star managers, Michael, is making misleading claims about his regional market share. Michael recently claimed that his office is the sole paper provider to 45% of its region's businesses. When the senior management conducted its own survey, they found that 36% of 180 randomly sampled businesses purchased their paper from Michael's office. Does this provide strong evidence that Michael is misleading the upper management about his office's performance? Conduct a full hypothesis test at the 5% level of significance.
1. My sample consists of ________ observations.
(a) suitably chosen
(b) independant
2. My sample consists of _______ .
(a) randomly selected observations from the population
(b) self selected responses
3. What is the appropriate pair of hypotheses to ans. this ques.? [HINT: it is NOT Ho: p = 0.45, Ha: p 0.45]
4. What is the value of the test statistic?
5. What is the p-value associated with this hypothesis test?
Explanation / Answer
(1) My sample consists of independent observations.
(2) My sample consists of randomly selected observations from the population
(3) Ho: p versus Ha: p < 0.45
(4)
Data:
n = 180
p = 0.45
p' = 0.36
Hypotheses:
Ho: p 0.45
Ha: p < 0.45
Decision Rule:
= 0.05
Critical z- score = -1.6449
Reject Ho if z < -1.6449
Test Statistic:
SE = {p (1 - p)/n} = (0.45 * (1 - 0.45)/180) = 0.0371
z = (p' - p)/SE = (0.36 - 0.45)/0.0370809924354783 = -2.4271
(5) p- value = 0.0076
Decision (in terms of the hypotheses):
Since -2.4271 < -1.6449 we reject Ho and accept Ha
Conclusion (in terms of the problem):
There is sufficient evidence that Michael's claim is false.
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