Stat Paper For 2 Year
Stat Paper For 2 Year
Stat Paper For 2 Year
Max. Marks: 17 Statistics: Paper II (Objective Type) Time Allowed: 20 Minutes Roll No. _______
Note: Four possible answers A, B, C and D to each question are given. The choice which you think is correct, fill that circle in front
of that question with Marker or pen ink. Cutting or filling two or more circles will result in zero mark in that question .
I. If 𝜇 = 5 𝑎𝑛𝑑 𝜎 2 = 2.25, what would be the value of 𝑆. 𝐸(𝑋̅), if samples of size 4 are drawn with replacement.
II. What do you understand by simple random sampling
III. If N=5, n=3 and 𝜎 2 =28, what will be the standard error of sampling without replacement
IV. If a=130, b=3.956, then estimate Y for X=12
V. If byx= -1.796 and bxy= -0.076, what will be the value of rxy?
VI. Given n=15, Sx=7.933 , Sy=16.627, ∑(𝑋 − 𝑋̅)(𝑌 − 𝑌̅) = 148 , compute bxy and byx
VII. Given rxy=-0.8, bxy=-0.45, what would be then value of byx?
VIII. Interpret the meaning of r =1 and r = 0
IX. It is known that rxy=0.48 find i) ryx ii) ruv where u=6x and v=7-3y
X. For a given set of data the two estimated regression lines are 𝑋̂ = 16.2 − 0.785𝑌 and 𝑌̂ = 20.8 − 0.219𝑋, find
the product moment correlation coefficient
XI. The value of 𝜇 𝑎𝑛𝑑 𝜎 2 are 50 and 250 respectively. Find 𝜇𝑋̅ and 𝜎𝑋2̅ when sample of size 50 is drawn with
replacement.
XII. Define sampled and target population
1 a) If X is normally distributed with mean=25 and variance=16, then find the probability
i) 𝑝(18 ≤ 𝑋 ≤ 22) ii) 𝑝(𝑋 ≥ 30) iii) 𝑝(𝑋 ≤ 16)
b) If “Z” is N( 0; 1) then find P(-2<Z<+2)
2 a) Ten students spend the following time in hours on their studies during a week: 35, 40, 17, 23, 50, 45, 30, 20, 18
and 22. Test the hypothesis 𝐻0 : 𝜇 ≤ 20 at 𝛼 = 5%
b) A sample of 15 measurements of weights (kg) gave a mean of 150 kg and standard deviation =25. Find 95%
confidence limits for the actual mean weight.
3 a) For a set of 8 pairs of values, we have ∑ 𝑋 = 448, ∑ 𝑌 = 472, ∑ 𝑌 2 = 40000, ∑ 𝑋𝑌 = 26762, Sx=16.67, find
the two regression coefficients
X 21 22 23 24 25 26
Y 25 24 23 22 26 27
Female 120 45 35
Do the data suggest association between education and gender? Use 5% level of significance
b) For the following time series, determine the trend values by using the method of least-squares for filling a
straight line.
Year 1921 1922 1923 1924 1925 1926 1927
5 a) A population consists of five numbers 3, 7, 11, 15, 19. Take all possible samples of size two with replacement
from this population. Find the mean and standard deviation of the sampling distributions of means and verify your
results
b) A population consists of six members. Marital status of each member is gives below
Member 1 2 3 4 5 6
Marital Status M S M S S S