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Notes-1

1. In order to find the correlation coefficient between two variables X and Y from 20 pairs of
observations, the following calculations were made :
∑x = 15, ∑y = - 6, ∑xy = 50
∑x2 = 61 and ∑y2 = 90
Calculate the correlation coefficient and the slope of the regression line of Y on X.

2. Suppose 2% of the items made in a factory are defective. Find the probability that there are
(i) 3 defectives in a sample of 100,
(ii) no defectives in a sample of 50.

3. Telephone Directories have telephone numberswhich are the combinations of the ten digits 0 to
9. The observer notes the frequency of occurrence of these digits and wants to test whether the
digits occur with same frequency or not (a = 0-05).The data are given below:
Digits     Frequency
0               99
1              100
2               82
3               65
4               50
5               77
6               88
7               57
8               82
9               30
(Given that x  (0.05) = 16.918)

4. Fit a linear trend y = a + b * Demand, to the data collected in a unit manufacturing umbrellas,
given in the following table :
Month 1 2 3 4 5 6
Demand 46 56 54 43 57 56

5. The mean weekly sales of soap bars in different departmental stores was 146.3 bars per store.
After an advertisement campaign the mean weekly sales of 22 stores for a typical week increased to 153.7 and showed a standard deviation of 17.2. Was the advertisement campaign successful at 5% level of significance ? (Given t 21 (0.05) = 2.08)

6. Write two merits and two demerits of Median.An incomplete frequency distribution is given as
follows
C.I.         Frequency
10 - 20        12
20 - 30        30
30 - 40         ?
40 - 50        65
50 - 60         ?
60 - 70        25
70 - 80        18
Given that median value of 200 observations is 46, determine the missing frequencies using the
median formula.

7. A chemical firm wants to determine how fourcatalysts differ in yield. The firm runs the experiment in three of its plants, types A, B, C. In each plant, the yield is measured with each catalyst. The yield (in quintals) are as follows :

Plant        Catalyst
1 2 3 4
A               2 1 2 4
B               3 2 1 3
C               1 3 3 1
Perform an ANOVA and comment whether the yield due to a particular catalyst is significant or
not at 5% level of significance. Given F3,6 = 4.76.

8. Find and plot the regression line of y on x on scatter diagram for the data given below :

Speed km/hr             30   40   50   60
Stopping
distance in feet        160 240 330 435

9. In an air pollution study, a random sample of 200 households was selected from each of 2 communities. The respondent in each house was asked whether or not anyone in the house was
bothered by air pollution. The responses are tabulated below (Given x21 (0.05) = 3.841) :
Community    Yes    No    Total
I               43    157     200
II               81    119     200
Total           124   276     400
Can the researchers conclude that the 2 communities are bothered differently by air pollution ? (𝛼 = 0.05)

10. The Police plans to enforce speed limits by using radar traps at 4 different locations within the
city. limits. The radar traps at each of the locations L 1, L2, L3 and L4 are operated 40%,30%, 20%, and 30% of the time. If a person who is speeding on his way to work has probabilities of
0.2, 0.1, 0.5 and 0.2 respectively, of passing through these locations, what is the probability
that he will receive a speeding ticket ? Find also the ptobability that he will receive a speeding
ticket at locations L 1, L2, L3 and L4.

Notes-2

1. Write any two merits and demerits of Arithmetic Mean. Given below is the data about the number
of seeds in a pod of a certain plant. Find the variance :
No. of Seeds   1   2   3   4   5
Frequency       8  14  7  12  3

2. Division A and B in a school have 20 students each. One student is to be selected from each
division. What is the probability that Rahul in division .A will be selected, if 2 students are selected out of 40 students ?

3. A die is rolled 1200 times with the following results :
No. that comes up : 1       2     3     4       5      6
Frequency :           195  289  202  242  163  109
Test, if the die . is unbiased at 5% level of significance. (Given that x 0.05 (5) = 11.07)

4. Define simple random sampling. Describe the limitations of simple random sampling.Differentiate SRSWR and SRSWOR methods of simple random sampling.

5. Cancer is present in 22% of a population and is not present in the remaining 78%. An imperfect
clinical test successfully detects the disease and with probability 0-70. Thus, if a person has the
disease in the serious form, the probability is 0.70 that the test will be positive and it is 0.30 if the
test is negative. Moreover among the unaffected persons, the probability that the test will be
positive is 0.05. A person selected at random from the population is given the test and the result is
positive. What is the probability that this person has the cancer ?

6. The probability that Meena is on time to catch the bus to her office is 0.8. Find the probability
that she is late
(a) exactly twice in a 6-day week, and
(b) at least once in a 6-day week.

7. In a partially destroyed laboratory, record of an analysis of correlation of data, only the following
results are legible :
Variance of x = 9. Regression equations
(i) 8x - l0y + 66 = 0
(ii) 40x - 18y - 214 = 0
What were :
(a) the means of x and y,
(b) the coefficient of correlation between x and y,
(c) the standard deviation of y ?

8. The following table shows the sample values of 3 independent normal random variables, X 1, X2
and X3 . Assuming that they have equal variances, and X test the hypothesis that they have the same mean by using ANOVA (Given F(2,9)(0.05) = 4.26) :
X1 :  13  11  16  22
X2 :  16  08  21  11
X3 :  15  12  25  10

9. The following table gives, for a sample of married women, the level of education and marriage
Low      High     Very High
Middle School   25        05            10
Level of Education        High School      50        30            40
College High    120       60            60

Can you conclude from the above, the higher the level of education, the greater is the degree of
adjustment in marriage ? Given x 2 (4, 0.05) = 9.488.

10. A population of size 500 is divided into 4 strata.The following table gives the data on size and
standard deviation of each stratum :
Strata
I     II      III      IV
Size 100  150   150    100
Standard Deviation 05   08     07     10
A stratified random sample of size 100 is to be drawn from the population. Determine the size of
samples from each of these strata for :
(a) Proportional Allocation,
(b) Neyman's optimum allocation.