Question

1. Following are observed frequencies. The null hypothesis is =:H0p1=, 0.30p2=, 0.35p3=, 0.05p4=, 0.05p50.25

Category	1	2	3	4	5
Observed	71	91	22	21	75

P-VALUE =_________

2. For the following observed and expected frequencies:

Observed	31	39	37	34	37	42
Expected	22	29	34	30	28	36

P-VALUE =________

3. Are you smarter than your older brother? In a study of birth order and intelligence, IQ tests were given to 18- and 19-year-old men to estimate the size of the difference, if any, between the mean IQs of firstborn sons and secondborn sons. The following data for 10 firstborn sons and 10 secondborn sons are consistent with the means and standard deviations reported in the article. Assume that the samples come from normal populations.
   
   

Firstborn
113.4	92.7	115.3	105.6	131.6
98.8	125.4	117.7	92.6	110.2

Secondborn
106.1	112.3	91.9	114.1	104
106.1	92.9	101.7	128.8	119.8

Ho = o2

H1 < o2

Left tailed test

CRITICAL VALUE =________

Answer 1

The null hypothesis is =:H0: p1= 0.30, p2 = 0.35, p3= 0.05, p4 = 0.05, p5 = 0.25

Category	Observed	Expected	(O-E)^2/E
1	71	84	2.011905
2	91	98	0.5
3	22	14	4.571429
4	21	14	3.5
5	75	70	0.357143
Total	280	280	10.94048

P-value = 0.0272

Category	observed	Expected	(O-E)^2/E
1	31	22	3.681818
2	39	29	3.448276
3	37	34	0.264706
4	34	30	0.533333
5	37	28	2.892857
6	42	36	1
Total			11.82099

= 11.82

P-value = 0.0370

sl no.	First born	second born
1	113.4	106.1
2	92.7	112.3
3	115.3	91.9
4	105.6	114.1
5	131.6	104
6	98.8	106.1
7	125.4	92.9
8	117.7	101.7
9	92.6	128.8
10	110.2	119.8
Total	1103.3	1077.7
Mean	110.33	107.77
sd	13.11683	11.43669047

test statistic is given by,

t = 0.415

Left tailed test.

Critical value, - 1.734 at level 0.05.

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