Suppose a scheduled airline flight must average at least 61% occupancy in order to be profitable to the airline. Occupancy rates were recorded daily for a regularly scheduled flight on each of 120 days, showing a mean occupancy per flight of 58% and a standard deviation of 9%.
(a)
If μ is the mean occupancy per flight and if the company wishes to determine whether or not this scheduled flight is unprofitable, give the alternative and the null hypotheses for the test.
H0: μ = 61 versus Ha: μ > 61
H0: μ = 61 versus Ha: μ ≠ 61
H0: μ = 61 versus Ha: μ < 61
H0: μ ≠ 61 versus Ha: μ = 61
H0: μ < 61 versus Ha: μ > 61
(b)
Does the alternative hypothesis in part (a) imply a one- or two-tailed test? Explain.
Since only large values of x would tend to disprove the null hypothesis, this is a two-tailed test.
(c)
Do the occupancy data for the 120 flights suggest that this scheduled flight is unprofitable? Test using α = 0.05. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)
test statistic z = rejection region z > z <
State your conclusion.
H0 is rejected. There is sufficient evidence to indicate that the flight is unprofitable.
H0 is not rejected. There is sufficient evidence to indicate that the flight is unprofitable.
H0 is rejected. There is insufficient evidence to indicate that the flight is unprofitable.
H0 is not rejected. There is insufficient evidence to indicate that the flight is unprofitable.