00:01
Hi guys in this problem we need to find and test the claims that supplier 2 provides gears with higher mean impact strengths so we have a null hypothesis such that mu 1 equals mu 2 and h1 such that mu 1 less than mu 2 okay we need to use the level of significance alpha with 0 .05 okay so we will reject each node if the p value is less than 0 .05.
00:37
Okay, okay.
00:40
Now let's find a t node, okay, which is x1 minus x2, x1 par minus x2 par, minus mu 2, minus mu 2, okay, over the square root of s1 squared over n1.
01:01
Plus s2 squared over n2 okay so we know that n1 equals 10 x1 par equals 290 and s1 equals 12 and for the supplier 2 we need to we know that n2 equals 16 x2 par is 3 to 1 and s 2 equals 1 and s 2 equals 16 x2 par is 3 to 1 and s 2 equals as well as 22.
01:33
So after the substitution here we can get a t node equals negative 4 .64.
01:41
Okay, so now let's compute the degrees of freedom.
01:46
Degrees of freedom here is just s1 squared over n1 plus s2 squared over n2 okay all squared over s squared over s squared over s over n1 all squared over n1 minus 1 plus s2 squared over n2 all squared over n2 minus 1 okay so after substitution we can get that it's 2 3 .7212 so we can round it up to uh can round it down to 23 okay okay so using the excel function, we can get that the p value equals 0 .005.
02:47
Okay.
02:49
So here we see that the p value is less than the level of significance.
02:53
So we should reject the null hypothesis and conclude that there is enough evidence to support that supplier tool provides gears with a higher mean impact strengths.
03:04
Okay.
03:05
Now for part b we have a new null hypothesis which is mu 1 minus mu 2 equals negative 25 and the alternative hypothesis such that mu 1 minus mu 2 is less than negative 25...