Question

There are 180 primary schools in a country area having an average of 30 or more people under the age of 21 per class. A sample of 30 schools drawn using systematic sampling with an interval of k= 6.

Serial number	1	2	3	4	5	6	7	8	9	10
No. of students	60	200	45	50	40	79	35	41	30	120
Serial number	11	12	13	14	15	16	17	18	19	20
No. of students	300	65	111	120	200	42	51	67	32	40
Serial number	21	22	23	24	25	26	27	28	29	30
No. of students	46	55	250	100	63	90	47	82	31	50

1. Estimate total number of students.
2. Estimate average number of students per farm.
3. The variance of the sample mean of students per farm.
4. 95% confidence interval for the total number of students.

Answer 1

Solution (1) Errimate the total no. of students ; K=6 No. of schools (0) - 30 30 ŷ KEyi = 6x2542 = 15252 • 15858 form, Estimate. average number of students per ģ= {k: 2,4} 15253 = 84.733 180 y = 84.733 (0) Variance of the sample mean of students per farm, Variance (Y) = N-D. ΧΣς nN Z CY:-7) 0-) $=. (60-84•733) + (200-8467335+ (45-84.733)'+ '+ (50 - 84.733)+(50-84733) + (31 – 84.733)+ (50-84.733) + 30 - 1 S 133307.8667 -4596.822 30-1 Standard deviation (S)-. 4596.822 = 67. 79

var(9)N-n Esr. MN 180-30 x 4596.822 30x(180) 150 X 4596.822 5400 z 12706895 var(y) = 127.6895 4) 95% confidence Interval for total students CI-X-0.95 1-0.95 -0.05 덧 a = = 20.025=196. ( By using the cronical valuer of a) confidence Interval 951. CI- 9 = 7 4 2 4 5 6 - (840733) + 4096 x 67.79 30 (60:47, 108.9913) - 60.47 lower Bound upper Bound - 108.991