00:01
The following information about the samples has been provided.
00:06
Now, first, the sample mean denoted by x1 is given us 3 .27 and x2 is given as 2 .33.
00:21
The sample deviation, samples channel deviation, denoted by s1 is equal to 1 .31 and sample deviation is equal to 1 .3.
00:31
2 .1 .1 .6.
00:34
Similarly, sample size n1 is equal to 25 and n2 is equal to 21.
00:40
So for the given data, as shown here, the null and alternative hypothesis will be null hypothesis denoted by h.
00:49
No one is equal to the u2 and the itemated hypothesis demoted by hha is is new one is not equal to null.
00:58
This corresponds to a two -tailed test for which as corresponds to a two -tailed pest for which the t test for two population means with two independent standards with unknown population standard deviations will be used.
01:18
Therefore this is the required solution for part one.
01:22
Now next coming to part b now next the degree degrees of freedom can be calculated as n minus 1.
01:32
But since here we have two sample sizes, therefore the degrees of freedom will be calculated as n1 plus n2 minus 2, which is equal to 25 plus 21 minus 2.
01:50
Therefore degrees of freedom denoted by the f is equal to 44.
01:54
Now next, calculating the critical value.
02:02
Based on the information provided, the significance level alpha is equal to 0 .05 and the decrease of freedom d of is equal to 44.
02:12
Therefore, the critical value for this two tail test, tc, is equal to 2 .0554 and this value is derived from the t value table.
02:25
This can be found either by using excel or the t distribution table...