B.Com. III (Semester (CGPA) Examination, 2018
STATISTICS (Paper II)
Advanced Statistics
Day and Date Saturday, 8-12-2018 Max. Marks 70
Time 10.30 a.m. to 1.00 p.m.
Instructions All questions are compulsory and carry equal marks.
Figures to the right indicate full marks.
1. Choose the most appropriate alternative amongst the given for each question. 14
Critical region is
region of rejecting H0 region of accepting H0
region of no decision none of these
The type I error is
rejecting H0 when H0 is true accepting H0 when H0 is true
rejecting H1 when H1 is true accepting H1 when H1 is true
When the null hypothesis is which of the following is one sided
alternative

Level of significance is always the probability of
type I error type II error
not committing error none of these
For testing goodness of fit the test used is
Z test t test
F test Chi-square test
If the test statistic Z is then for testing against two sided alternative
at α reject H0 if
1.96 1.64 1.96 Z 1.96
Equality of two population variances can be tested by
Z test Chi-square test
t test F test
Range of F variate is
∞ to ∞ 0 to 1 0 to ∞ ∞ to 0
To test equality of means of several normal populations, the test to be used is
t test Chi-square-test
F test Z test
10) Degrees of freedom for Chi-square statistic in case of contingency table of
order r × s is
rs
rs 1 1
11) A set of all possible individuals under study is called
a population a sample a group none of these
12) Paired t-test is applicable when the observations in the two samples are
paired correlated
equal in number all of these
13) Whether a test is one sided or two sided, depends on
alternative hypothesis composite hypothesis
null hypothesis simple hypothesis
14) Any hypothesis which is complementary to the null hypothesis is
Simple hypothesis Composite hypothesis
Alternative hypothesis None of these
2. Explain the procedure to test the hypothesis H0 versus H1
for large samples, at level of significance. 7
Define t variate. Explain the applications of t distribution. 7
3. Explain the paired t-test for testing the significance of difference between
two means. 7
Define the terms parameter, statistic, simple hypothesis and composite
hypothesis. 7
4. Attempt any one of the following 14
Define F variate. State its p.d.f. and various applications of F distribution.
Also explain one of these in detail.
Daily sales figures of 40 shopkeepers showed that their average sales
and standard deviation were Rs. 528 and Rs. 600 respectively. Is the
assertion that daily sale on the average is Rs. 400 contradicted at level
of significance by the sample
5. Attempt any one of the following 14
Define Chi-square variate. State its p.d.f. and explain the test procedure to
test the goodness of fit.
The machine producing ball bearing is operating properly if the variance
of the diameter is 1.44 square cm. A random sample of 14 ball bearings
showed variance of 2.08 square cm. Will you conclude that the machine is
operating properly based on these data Given X214 0 05: . 23.685.