Question

1) A sample of 12 recent births at a local hospital in a small town has the following birth weights (in ounces): 89, 122, 137, 144, 98, 113, 124, 138, 108, 117, 105, 99

a) Compute the sample mean and standard deviation of the birth weights. (You can use technology to find this.)

b) Assume the population distribution of birth weight is approximately normal. Construct the 95% confidence interval to estimate the mean birth weight of all babies born in this small town. (Should you use a t-score or a z-score?)

2) In a study of possible correlation between the height, x in cm and the weight, y in kg, of chimpanzees, a sample of 40 animals produces a correlation coefficient of ? = 0.813, and a regression line with equation ? = 0.34? + 19.5. What is the expected weight of a 80 cm tall chimpanzee?

a) 177.9??

b)57.1??

c) 24.0??

d) 46.7??

3) In #2, what does the correlation coefficient tell you?

a) There is no linear correlation between the height and weight of a chimpanzee.
b) That for every 1 cm more in height a chimpanzee is, it weighs 0.813 more kg.
c) There is a weak positive linear correlation between the height and weight of a chimpanzee. d) That for every 1 kg more in weight a chimpanzee is, it is 0.813 cm taller.
e) There is a strong positive linear correlation between the height and weight of a chimpanzee.

Answer 1

a) We would be using the sample mean sample standard deviation here as:

S.No.	X	(X - Mean(X))^2
1	89	738.027777
2	122	34.02777778
3	137	434.0277778
4	144	774.6944444
5	98	330.0277778
6	113	10.02777778
7	124	61.36111111
8	138	476.6944444
9	108	66.69444444
10	117	0.694444444
11	105	124.6944444
12	99	294.6944444
	1394	3345.666667

b) As we dont know the population standard deviation here but the sample standard deviation, we will use the t distribution here for n - 1= 11 degrees of freedom as:

P(t11 < 2.201) = 0.975

Therefore, due to symmetry, we get here:
P( -2.201 < t11 < 2.201) = 0.95

Therefore the confidence interval here is obtained as:

This is the required 95% confidence interval for population mean here.