Page 448 - DMTH404_STATISTICS

Statistics

Notes 2
s
4. The 100(1 - a)% ................. for the variance ratio 1 2 , are given by
s
2
s é 2 1 s 2 s 2 1 ù
-
P ê 1 ×  1  1 × ú = 1 a .
2 2 2
s ê ë F s s F
-
2 a /2 2 2 1 a /2 ú û
32.8 Review Questions
1. Test the hypothesis that s = 8, given that S = 10 for a random sample of size 51. Also
construct 95% confidence interval for s.

Hint : Use a two tailed normal test.
2. A random sample of size 10 from a normal population gave the following observations :
169, 173, 171, 177, 161, 163, 174, 168, 172, 165.

Test the hypothesis that population variance is 25.
2
Hint : Use a two tailed c test.
3. The following two samples are drawn from two normal populations. Test at 5% level of
significance whether their variance can be regarded as equal?
Sample I : 60, 65, 71, 74, 76, 82, 85, 57.
Sample II : 61, 66, 67, 85, 78, 63, 85, 86, 88, 91.
Hint : Use F - test.

4. Can the following two samples obtained from two normal populations, be regarded to
have same variances?
Sample No. Sample Size Sample Variance
1 15 20
2 25 35

Test at 10% level of significance.
Hint : Use F - test.
5. Two independent random samples, one of 12 observations with mean 15 and sum of
squares of deviations from mean equal to 135 and another of 16 observations with mean
22 and sum of squares of deviations from mean equal to 250, were obtained from two
normal populations. Test at 5% level of significance whether the two samples can be
regarded to have come form the same population?

Hint : Test s = s and  =  an in example 34.
1 2 1 2
6. The following figures relate to the number of units produced per shift by two workers
A and B for a number of days:

A : 19, 22, 24, 27, 24, 18, 20, 19 and 25.
B : 26, 37, 40, 35, 30, 30, 40, 26, 30, 35 and 45.
Can it be inferred that A is more stable worker compared to B? Answer using 5% level of
significance.
Hint : Use F - test.

440 LOVELY PROFESSIONAL UNIVERSITY