The dataset lowbwt contains information recorded for a sample of 100 low birth weight infants born in two teaching hospitals in Boston. Measurements of systolic blood pressure are saved under the variable named sbp, while indicators of gender-- 1 indicating a male and 0 indicating a female-- are saved under the variable name sex.

a. Compute a 95% confidence interval for the true mean systolic blood pressure of male low birth weight infants.

b. Compute a 95% confidence interval for the true mean systolic blood pressure of female low birth weight infants.

c. Do you think it's possible that males and females have the same mean systolic blood pressure? Explain briefly.

d. Calculate 90% confidence intervals for both male and female low birth weight infants (two separate intervals).

e. Calculate a 99% confidence interval for both male and female low birth weight infants (two separate intervals).

f. Suppose the standard deviation () of the larger population of low birth weight infants is known to be 11 mm. Construct 95% confidence intervals for males and females using this.

g. How does the interval calculated based on differ from the 95% interval based on s?

lowbwt (2) 100 entries
sbp	sex	tox	grmhem	gestage	apgar5
43	1	0	0	29	7
51	1	0	0	31	8
42	0	0	0	33	0
39	0	0	0	31	8
48	0	1	0	30	7
31	1	0	1	25	0
31	1	1	0	27	7
40	0	0	0	29	9
57	0	0	0	28	6
64	0	1	0	29	9
46	0	0	0	26	7
47	0	0	1	30	6
63	0	0	0	29	8
56	0	0	0	29	1
49	1	0	0	29	8
87	1	0	0	29	7
46	0	0	0	29	8
66	0	0	0	33	8
42	0	1	0	33	8
52	0	0	0	29	7
51	1	0	0	28	7
47	0	0	0	30	9
54	1	0	0	27	4
64	1	0	0	33	9
37	0	0	0	32	7
36	1	1	0	28	3
45	0	0	1	29	7
39	1	0	0	28	7
29	0	0	0	29	4
61	0	0	0	30	3
53	1	0	0	31	7
64	0	0	0	30	7
35	0	0	0	31	6
34	1	0	0	29	9
62	0	0	0	27	7
59	0	0	0	27	8
36	1	0	0	27	9
47	0	0	0	32	8
45	1	0	1	31	2
62	0	0	1	28	5
75	1	1	0	30	7
44	1	0	0	29	0
39	1	0	0	28	8
48	0	0	1	31	7
43	0	1	0	27	6
19	0	0	1	25	4
63	1	0	0	30	7
42	1	0	0	28	6
44	0	0	0	28	9
25	0	0	0	25	8
26	0	0	0	23	8
27	1	0	0	27	9
35	1	0	0	28	8
40	1	0	0	27	7
44	0	0	0	27	6
66	1	0	0	26	8
59	0	0	0	25	3
24	0	0	0	23	7
40	0	0	1	26	3
49	0	0	0	24	5
53	1	1	0	29	9
45	0	0	0	29	9
50	1	0	1	27	8
64	1	0	0	30	7
48	0	0	0	30	6
48	0	0	1	32	4
58	0	1	0	33	7
67	0	0	0	27	8
40	0	0	1	31	8
48	0	0	0	26	8
36	1	0	0	27	5
44	1	0	0	27	6
53	0	1	0	35	9
45	0	1	0	28	6
54	1	0	0	30	8
44	1	1	0	31	2
42	1	0	0	30	5
50	0	0	0	27	0
48	0	0	0	25	5
29	0	0	1	25	5
30	0	0	1	26	2
36	0	0	0	29	0
44	0	0	0	29	0
46	0	1	0	34	9
51	1	1	0	30	4
51	1	0	0	29	5
43	1	1	0	33	7
48	1	0	0	30	5
52	1	0	0	29	8
43	1	0	0	24	6
42	1	1	0	33	8
48	1	0	1	25	5
49	0	1	0	32	8
62	1	1	0	31	7
45	1	0	0	31	9
51	0	1	1	31	6
52	1	0	0	29	8
47	1	1	0	32	5
40	0	1	0	33	8
50	0	0	0	28	7