00:01
All right, so in the given question, we have been asked to conduct a hypothesis test.
00:06
So here our null hypothesis is that population average is 6.
00:10
And the alternative hypothesis is that the population averages less than 6.
00:15
So this is a left -tailed hypothesis test.
00:19
Right.
00:19
So what information is provided to us? the size of the sample here is 5.
00:24
The sample mean is 4 .9 and the sample standard deviation is 1 .4.
00:29
So the value of population standard deviation is unknown which means that we'll use the t test.
00:36
Now first part of the question here is to determine the rejection region.
00:40
So alpha here is 0 .10.
00:44
So our critical value in this case this corresponds to the value of t alpha and minus 1.
00:49
So this will be t0 .10 .10 and 4.
00:53
So here this value is minus 1 .533.
00:57
Right? so our rejection region will be that we will reject the null hypothesis if the test statistic value is less than minus 1 .533...