In February 2012, the mean cost of an airline round-trip with a discount fare wa
ID: 3128562 • Letter: I
Question
In February 2012, the mean cost of an airline round-trip with a discount fare was $258. A random sample of 15 round-trip discount fares during the month of March provided the following data: 310 260 265 255 300 310 230 250 265 280 290 240 285 250 260
a. Do these data indicate that the mean round-trip discount fare has increased in March? Establish the appropriate null and alternative hypotheses to test this assumption. b. What conclusion should be drawn? Use a level of significance of 0.05. Make sure to state the decision rule.
Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u <= 258
Ha: u > 258 [ANSWER]
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b)
As we can see, this is a right tailed test.
Thus, getting the critical t,
df = n - 1 = 14
tcrit = + 1.761310136
Hence, we reject Ho when t > 1.761.
Getting the test statistic, as
X = sample mean = 270
uo = hypothesized mean = 258
n = sample size = 15
s = standard deviation = 24.78478796
Thus, t = (X - uo) * sqrt(n) / s = 1.87517441
As t > 1.761, we REJECT THE NULL HYPOTHESIS.
Hence, there is significant evidence that the mean round-trip discount fare has increased in March at 0.05 level. [CONCLUSION]