00:01
So, there are a bunch of questions here that we need to answer.
00:05
The given data set and the test we have to employ is paired samples t -test.
00:12
So, let's calculate step by step the given questions in here.
00:18
So, the first step is to calculate the differences and to find out the mean of the differences and the standard deviation of the differences.
00:29
So, the mean of the differences can be found out by calculating the individual differences first.
00:35
So, the differences for each of the samples are for the first one it's minus 15 and for the second one it's minus 21 and then for the third sample it's minus 25 and then it's 1 and then finally it's minus 6.
01:03
So, once we have the differences the mean difference is minus 15 minus 21 minus 25 plus 1 minus 6 divided by 5.
01:16
So, this comes out to be minus 13 .2.
01:21
Now, standard deviation can be calculated using the formula square root of sigma i equals to 1 to n di minus the mean of the differences divided by n minus 1 because this is the standard deviation of a sample.
01:38
So, upon calculating this we would get the standard deviation as and this comes out to be 10 .69.
01:47
Now, the null and alternative hypothesis in symbols can be written for the given question as mu d equals to 0 and the alternative hypothesis is the difference of means in the population is not equal to 0.
02:07
Now, the same statement can be written in can be written as the following sentences which is there is no significant difference between actual and forecast temperatures.
02:40
Similarly, the alternative hypothesis can be written as there is a significant difference between actual and forecast temperatures.
03:07
So, that is the fourth question.
03:09
Now type of tail since the alternative hypothesis includes not equal to it's a two sided test.
03:24
It's a two sided or better put it's a two tailed test.
03:35
Now on to the next question critical value...