Question

chi-square test statistic = ________

Short answer

chi-square test statistic =$36$

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 test statistics can be calculated by using the formula shown below:

Test statistic$=\frac{(n-1)s^2}{{\sigma }^2}$

Here,

$n-$sample size

$s^2-$sample variance

${\sigma }^2-$population variance

Therefore, the calculation is shown below:

Test statistic

$=\frac{(25-1)(15{)}^2}{\left(150\right)}$

$=\frac{24\times 225}{150}$

$=36$