00:01
Hello students, according to the given question, we have to find the test value.
00:10
So the null hypothesis h0 such that mu is equal to 6 .0 and alternative hypothesis h1 such that mu is less than 6 .0.
00:24
So they have given alpha is equal to 0 .05 and n will be equal to they have given 12 values.
00:33
So n will be 12.
00:35
So from the given data, the mean of the difference, that is, d i will be calculated as xi minus yi.
00:44
So here xi represents the radial tires and yi represents the belted, belted tires.
00:59
So summation di value will be equal to summation of x i minus yi.
01:05
So by subtracting the values we get 4 .2 minus 4 .1 up to the last term that is 5 .2 minus 4 .9.
01:18
So which is equal to the value 1 .7.
01:23
So d bar will be equal to 1 by n summation d i.
01:28
So which is equal to 1 by 12 into 1 .7.
01:32
So which is equal to 0 .1417.
01:36
Now summation, ti minus d bar whole square value will be equal to 0 .1 minus 0 .151417 whole square plus up to the last term that is 0 .3 minus 0 .1417 whole square which is equal to 0 .4292.
02:05
Now standard deviation s d is equal to 1 by n minus 1 summation of d i minus d bar whole square under the square root...