00:01
So, we are given that the two samples.
00:06
First for wearing seat belt n1 is equals to 123.
00:13
Standard deviation is 1 is equals to 1 .77 and population mean x1 bar 0 .82.
00:20
And for not wearing seat belts, n2 is equal to 290, s2 is equal to 3 .06 and x2 bar is equal to 1 .39.
00:35
So, we have to solve only the part a in which we have to compute the hypothesis for null hypothesis as mu1 should be equal to mu2, the mean should be equal and alternative hypothesis will be mu1 less than 2 mu2.
00:55
So, for this the test statistics we are going to use t is equal to into the bracket formula says as x 1 bar minus or x 2 bar minus or mu 1 minus mu 2 that whole divided by the pooled standard deviation that is s 1 square by n 1 plus s 2 square divided by n 2 plugging all the values you will get 0 .83 minus 1 .39 then minus or now see this difference should be equals to 0 because we have taken here at mu1 is equals to mu2 so this should be equals to 0 divided by the under root over s1 square 1 .77 of whole square divided by n1 123 plus s2 square is 3 .06 of whole square divided by sample size is 290.
01:53
So after simplifying and solving the t statistics value will comes out negative of 2 .33 now, if you see that the degree of freedom has the formula that is s1 square by n1 plus s2 square by n2 that whole square divided by the 1 over n1 minus of 1 times of s1 whole square by n1 of whole square plus 1 by n2 minus of 1 into the bracket s2 whole square square by into of that whole square.
02:29
Let's plug in the values...