00:01
In this question, first we state the null and alternate hypothesis.
00:05
We have null hypothesis h0 is mean is equal to 30, i .e.
00:09
The mean time to complete the maze is 30 seconds.
00:12
And the alternate hypothesis hj is mean is not equal to 30, which means the mean time to complete the maze is not 30 seconds.
00:19
Now we have the level of significance alpha is equal to 0 .01.
00:24
Now we can calculate the test statistic for this sample.
00:29
We will use a one sample t -test since the population standard deviation is unknown and the sample size n is less than 30.
00:38
So we have t is equal to x -bar minus mu over s over square root of n.
00:44
Where we have x -bar value is equal to 39 .3, mu value is equal to 30, which is hypothesized population mean, and sample standard deviation is 2 .5, and sample size n is equal to 20.
00:59
Now using these parameters, we can calculate test statistic t is equal to 29 .3 minus 30 divided by 2 .5 over square root of 20.
01:09
On calculating this, we get test statistic t value is equal to negative 1 .788...