Page 378 - DMTH404_STATISTICS

Statistics

Notes 26.5 Self Assessment

1. Let  be coefficient of ................... in a bivariate normal population and r be its estimator
based on a sample of n observations (X , Y ).
i i
2. Let there be two ................... samples of sizes n and n from two normal populations with
1 2
correlations  and  respectively. Let r and r be the correlations computed from the
1 2 1 2
respective samples.
2
3. In addition to the use of  in tests of hypothesis concerning the standard deviation, it is
used as a test of ................... and as a test of independence of two attributes. These tests are
explained in the following sections.
 ................... can be used to test, how far the fitted or the expected frequencies are in agreement
with the observed frequencies.
26.6 Review Questions

1. We want to decide whether a cubic die is balanced or not. For this purpose the die is
thrown 300 times and various outcomes are recorded. If the observed frequencies of the
six faces, namely 1, 2, 3, 4, 5 and 6 are 35, 40, 32, 60, 68 and 65 respectively, can we conclude
that the die is unbiased?

Hint : The expected frequency of each face under H is 50.
0
2. Four coins are tossed 320 times and the number of heads obtained were recorded as
follows :

No. of heads : 0 1 2 3 4
Frequency : 15 102 108 68 27

Can we regard all the coins as unbiased?
Hint : Find expected frequencies of the number of heads on the assumption that the coins
are unbiased.

3. Three dice were thrown 80 times and the number of times 2, 4 or 6 was obtained, were
recorded as given below:

No. of dice showing 2,4 or 6 : 0 1 2 3
Frequency : 8 28 32 12
Test the hypothesis that all the three dice are fair.
Hint : Under H , the probability of success, i.e., getting 2 or 4 or 6 on a die is 0.5. If r denotes
0 4 4
the number of dice giving successes in a throw, we have p r a f = C 0.5 .
r
4. The health department of municipal corporation of a city believes that 14% persons of the
city are smokers as well as drinkers, 30% are drinkers while 40% are smokers. In a random
sample of 150 persons, it was found that 24 persons were smokers as well as drinkers, 21
were only drinkers and 36 were only smokers. Do the above data support the belief of the
department. Use 5% level of significance.
Hint : Use the figures of belief, given in percentages, to find the expected frequencies.

370 LOVELY PROFESSIONAL UNIVERSITY