Question

9. Measuring the length of a pipe with the same measurement instrument, the following results have been obtained: 47.25:49.01; 50.75:48. 14: 50.08; 47.98; 49.12: 48.56; 48.19; 49.85; 47.77; 49.32 48.45; 49.55; 48.48:50.50; 47.80; 48.70. Draw the histogram. 10. The mean value of 90 observations is 48.5 and with sample variance of 1.6. Find 96% confidence interval of the population standard deviation.

9 th and 10 questii will be one..because 9 th answer be a part in 10 th questions

Answer 1

9) For histogram we need to construct frequency table

Range = highest observation -lowest observation = 50.75-47.25 = 3.50

Let us construct a frequency table of 5 classes , width of each class = 3.5/5 = 0.70

Class	frequency
47.25-47.95	3
47.95-48.65	6
48.65-49.35	4
49.35-50.05	2
50.05-50.75	3

The histogram is given below

Histogram 7 6 5 4 3 N 1 0 [47.25, 47.95] (47.95, 48.65) (48.65, 49.35] (49.35, 50.05] (50.05, 50.75]

10 ) The 96% confidence interval for population standard deviation is

(n − 1)52 xa/2 (n − 1)s 2 1-a/2

For 96% confidence ,

= 0.04, a/2 = 0.02,1-a/2 = 0.98

degrees of freedom = n-1 = 90-1 =89

Thus

2 2 X0.02 118.49, X0,98 - 63.79
( from chi square table for 89 df )

Thus 96% confidence interval for population standard deviation

(90-111.6 118.49 (90-11.6 63.79

= (1.10 , 1.49)