An airline claims that the no-show rate for passengers is less than 5%. In a sam
ID: 3153389 • Letter: A
Question
An airline claims that the no-show rate for passengers is less than 5%. In a sample of 420 randomly selected reservations, 19 were no-shows. At a = 0.01, test the airline's claim. Round p to the nearest thousandth when calculating the test statistic. f Write the hypotheses to test this airlines' claim. Find the value of the z-test statistic. Find the p-value (probability) of the z-test statistic based on your hypotheses. Draw your conclusion. Make sure to write the conclusion in the context of the problem.Explanation / Answer
a)
Formulating the null and alternatuve hypotheses,
Ho: p >= 0.05
Ha: p < 0.05 [ANSWER]
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b)
As we see, the hypothesized po = 0.05
Getting the point estimate of p, p^,
p^ = x / n = 0.045238095
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.010634624
Getting the z statistic,
z = (p^ - po)/sp = -0.447773663 [ANSWER]
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c)
As this is a 1 tailed test, then, getting the p value,
p = 0.327158276 [ANSWER]
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d)
As P > 0.01, we FAIL TO REJECT THE NULL HYPOTHESIS.
Hence, there is no significant evidence to suuport the airline's claim that the no-show rate for passengers is less than 5%. [CONCLUSION]
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