00:02
Okay, so to test whether the average length of outgoing telephone calls from a business office has decreased after the policy changes, we can perform a one -sample t -test.
00:16
Okay, so in your specific case, the new hypothesis is that the average length of a call, mu, is 143, or excuse me, is 143 seconds or more.
00:40
And the alternative is that the average length of a call has decreased, which is mu less than 143.
00:50
And now we need to calculate the test statistic, which is given by x -bar minus mu0 over s over square root of n, where x -bar is the sample mean, which is 133 seconds, and mu nu is the hypothesized mean, which is 143.
01:12
We divide this by s over square root of n, where s is the sample standard deviation, which is 35 seconds, and n is the sample size, which is 100.
01:28
And this turns out to be negative 2 .86.
01:34
And now we need to find the critical value of t.
01:37
T.
01:37
So the critical value of t at the 1 % significance level with degrees of freedom n -1 equals 99 is t star negative 2 .365.
02:00
And you can find this value in any kind of t table table or on the internet as well.
02:08
So let's compare this value against the t statistic that we have.
02:14
So t equals negative 2 .86 and this is less than t star of negative 2 .365.
02:27
So this means that we reject the new hypothesis...