Question

The IRS claims that it takes 87 minutes to prepare a tax form. You believe it takes longer than 87 minutes. You ask 21 tax filers and find the following preparation times:

61, 69, 78, 79, 87, 89, 96, 96, 97, 98, 98, 99, 100, 100, 105, 108, 110, 117, 118, 120, 125

Determine if the preparation time is significantly longer than 87 minutes. Use α = .025.

Answer 1

Here we're testing $H_0:\mu \leq 87 \ vs \ H_a:\mu>87$

For this, we'll be using the t-test,

Where the test statistic is given by :

$T=\frac{\bar{x}-\mu}{\frac{S_x}{\sqrt(n)}}$

which follows t-distribution with a degree of freedom n-1 under Ho.

Here $\bar{x}=97.62 \ , S_x=16.515 \ while \ n=21$ .

Thus the test statistic is 2.9466. Now, here we're given $\alpha=0.025$ thus the critical value is $t_{20,0.975}=2.086$ .

Here test statistic is greater than the critical value hence we reject Ho. i.e there is sufficient evidence to support the claim that the mean i is greater than 87.