Question

Is this a right-tailed, left-tailed, or two-tailed test?

Short answer

The test is right-tailed test.

Step-by-step solution

Given information

Given in the question that, Suppose an airline claims that its flights are consistently on time with an average delay of at most $15$ minutes. It claims that the average delay is so consistent that the variance is no more than $150$ minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next$25$ flights. The average delay for those $25$ flights is $22$ minutes with a standard deviation of $15$ minutes.

Explanation

The null hypothesis is shown below:

$H_0:{\sigma }^2\le 150$

That is, the variance is no more than $150$.

Against the alternative hypothesis as shown below:

$H_a:{\sigma }^2>150$

That is, the variance is more than $150$.

The alternative hypothesis sign that is ">" tells that the test is right-tailed test.