An airline promotion to business travelers is based on the assumption that no mo
ID: 3151277 • Letter: A
Question
An airline promotion to business travelers is based on the assumption that no more than two-thirds of business travelers use a laptop computer on overnight business trips.
a. State the hypotheses that can be used to test the assumption.
H0: p
Ha: p
b. What is the sample proportion from an American Express-sponsored survey that found 366 of 547 business travelers use a laptop computer on overnight business trips (to 4 decimals)?
c. What is the p-value (to 4 decimals)?
d. Using = .05, can you conclude that the proportion of business travelers who use a laptop computer on overnight business trips is greater than two-thirds?
SelectYesNoItem 5
if you use a table, please specify which one used.
Explanation / Answer
a)
Formulating the null and alternatuve hypotheses,
Ho: p <= 0.666666667
Ha: p > 0.666666667 [ANSWER]
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b)
As we see, the hypothesized po = 0.666666667
Getting the point estimate of p, p^,
p^ = x / n = 366/547 = 0.669104205 [ANSWER]
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c)
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.020155802
Getting the z statistic,
z = (p^ - po)/sp = 0.12093481
As this is a 1 tailed test, then, getting the p value,
p = 0.451871335 [ANSWER]
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D)
significance level = 0.05
As P > 0.05, we FAIL TO REJECT THE NULL HYPOTHESIS.
There is no significant evidence that more than two-thirds of business travelers use a laptop computer on overnight business trips at 0.05 level. [CONCLUSION]
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As z distribution is used here, you could have used a z distribution table to get the right tailed area of z = 0.12.
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