00:01
Hello student in step 1 the correct answer is option a.
00:11
It is independent two sample t -test because here two samples are independent.
00:28
Independent variable are not on two level.
00:32
Variants are assumed to equal.
00:34
Hence we used independent sample t -test.
00:39
Now in step 2, we want to test the null hypothesis h naught such that mu1 less than or equal to mu2 against the alternative hypothesis h a such that mu1 greater than mu2.
01:01
Here we want to test whether students who study with music playing devote much attention to their studies than those studies who study under quiet conditions.
01:11
So here we consider population mean of students with music is less than population mean of students without music as null hypothesis.
01:19
Alternative hypothesis is opposite to null hypothesis.
01:26
Now in order to find the test statistic, let's compute x1 bar is equal to 5 .8 x2 bar is equal to 8 .1.
01:49
Then s1 is calculated as 1 .2293 s2 is calculated as 1 .4491.
01:59
Now the test statistic t is equal to x1 bar minus x2 bar divided by root of n1 minus 1 s1 square plus n2 minus 1 s2 square divided by n1 plus n2 minus 2 into 1 by n1 plus 1 by n2.
02:34
Substituting the values and simplifying we will get the test statistic t as minus 3 .827.
02:48
Therefore, t statistic is calculated as minus 3 .827.
02:57
Now in step 4, we want to find the critical t value.
03:03
Based on the information provided, we have alpha is equal to 0 .05 and the degrees of freedom is equal to 80.
03:24
Now assuming population variance are equal, hence the critical value for this right -tailed test is equal to 1 .734...