Fancy pets are big business, so a young entrepreneur (age...

Fancy pets are big business, so a young entrepreneur (age 12) decided to breed golden hamsters, a type well known to pet stores and collectors. (Oddly enough, nearly all golden hamsters in captivity are descendents of one litter found in Syria in 1930.) Of 47 recent litters, there were an average of 7.27 baby hamsters with a standard deviation of 2.5 hamsters per litter. (a) (7 points) Find and interpret a 90% confidence interval for the mean litter size. (b) (7 points) Teddy hamsters have an average of 5 baby hamsters per litter, is there evidence that golden hamsters have significantly larger litters than teddy hamsters? Use an ??-level of 0.01.

Transcript

00:01 Well, i couldn't resist doing this question for you because i just have so many hamster stories, which i won't share at all with you, but we had them and gerbils and all kinds of fun things have happened.

00:13 But the average of those 47 litters had 7 .27 little hamsters that are golden hamsters with a sample standard deviation of 2 .5.

00:23 And in part a, we want to find a 90 % confidence interval for the mean, which is the mean number of hamsters that a golden jerval have.

00:37 Or excuse me, a golden hamster will have.

00:38 So we take our 7 .27.

00:42 And then we need to find the t value that has 46 degrees of freedom and has 0 .05 in the upper tail.

00:51 And i'm going to use my t -cdf to find that.

00:55 And i'm actually going to put it in for my inverse t, i should say, said that the wrong way, and put 0 .05 in for the area.

01:03 And then my degrees of freedom will be 46.

01:06 And so it's going to give me a negative value, but this notation is to find the upper tail.

01:12 And so i end up getting 1 .67.

01:15 I'm going to round it to 9.

01:17 So for my confidence interval, i'm going to have my value, my x -bar, plus or minus my t value, which is that 1 .679.

01:26 And notice in your table you probably have 40 degrees of freedom.

01:30 That's what i have.

01:31 And if i look up 40 degrees of freedom, it's 1 .684.

01:36 This is just more accurate.

01:38 And then my sample standard deviation divided by the square root of 47.

01:43 And so 7 .27 minus 1 .679 times that 2 .5.

01:51 Divided by the square root of 47, and that's a lot of litters of hamsters...

Question

Please give Ace some feedback