Question

In 1996, the average airfare two weeks in advance on the flight between the cities of Veracruz and Mérida was $ 245.00. In a survey conducted in 1997, 90 travelers chosen at random between these two cities were found to have paid on average $ 218.77 with a standard deviation of $ 68.00. Did it significantly change the average air fare on this route between 1996 and 1997? What is the highest value of alpha for which you could reach the observed average rate is not significantly different from $ 235?

Answer 1

Here, we are testing whether the mean significantly changed from $245, therefore this is a two tailed test, the test statistic here is computed as:

Now as this is a two tailed test, the p-value here is computed as:

For (n-1) = 89 degrees of freedom, we get:

p = 2P( t₈₉ < -3.6594) = 2*0.0002 = 0.0004

As the p-value here is significantly less than any reasonable level of significance, therefore the test is significant and we can conclude that we have sufficient evidence that the mean significantly changed from $245.

Now for the second part, we are testing whether the mean has significantly changed from $235, therefore the test statistic here is computed as:

As this is a two tailed t test, the p-value here is computed as:

p = 2P( t₈₉ < -2.2643) = 2*0.013 = 0.026

Therefore the highest value of alpha required here is 0.026