This document appears to be a multiple choice quiz on quantitative techniques and statistics. It contains 36 multiple choice questions covering topics like correlation, normal distributions, probability, hypothesis testing, and regression. The questions range from calculating probabilities and percentages to identifying statistical concepts and relationships between variables based on data provided.

1. Page 1 of 4
Faculty: AMIR KHATRI
Quantitative Techniques ( Statistics)
Marks: 50
1. Which correletion indicates a strong positive line relationship?
a. 0.4 b. -0.75 c. 1.5 d. 0.99
2. For a npormal distribution with mean 20 & standard deviation 5, approximetly what percent of
the observations will be between 5 & 35?
a. 50% b. 68% c. 95% d.99.7%
3. In any normal distribution, the percent of observations falling between standard score z = 0 &
z = 2 is about:
a. 95% b. 81.5% c. 47.5% d. 50%
4. When you choose a card at random from a well shuffled deck, the probablility is ¼ that your
card belongs to any one of the four suits. The probablity that your card is red is:
a. 0 b. 1/4 c. 1/2 d. 3/4
5. A random survey of 300 students found that on average students spend 3.4 hours studying per
calss for finals with a standard deviation of 1.7 hours. A 99% confidence interval for the true
mean is:
a. 3.4 ± 0.25 b.3.4 ± 0.001 c. 1.7 ± 0.25 d. 1.7 ± 0.025
6. Which of the following events is/are likely to be independent?
a. Successive tosses of coin.
b.Successive selections of cards from a pack without replacement.
c. Gender & shoe size
d. Breakdown of machines of different types & ages.
7. The probability of a randomly selected individual being left handed is 0.10. two individuals are
randomly selected. What is the probablity that one individual is left handed & one individual is
right handed?
a. 0.18 b. 0.20 c. 0.90 d. 0.09
8. Event A occurs with the probablity 0.3 & events B occurs with probablity 0.4. If A & B are
independent, we may conclude:
a. P(A&B)=0.12 b.P(A/B)=0.3 c. P(B/A)=0.4 d.all of the above
9. A population has a mean of 103 & a standard deviation of 9. You select a sample of size 36.
a. The mean of the sampling distibution of 𝑥̅ 𝑖𝑠 103/√36
b.The standard deviation of the sampling distribution of 𝑥̅ 𝑖𝑠 9.
c. The mean of the sampling distribution of 𝑥̅ 𝑖𝑠 9.
d. The standard deviation of the sampling distribution of 𝑥̅ 𝑖𝑠 1.5
10. Which could be a correct statement of a null hypothesis?
a. 𝑥̅ = ±3 b. 𝑥̅ = −3 c. 𝑥̅ = 0 d. µ = -3
11. To calculate a z-test statistics for a hypothesis test, you do not need to:
a.calculate a sample mean b.know a sample size
c. state a null hypothesis d. calculate a sample standard deviation

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Faculty: AMIR KHATRI
12. In a test of 𝐻 𝑜: µ = µ 𝑜 vs. 𝐻1: µ ≠ µ 𝑜, at the α=0.05 level,you would reject 𝐻 𝑜 if
a.𝑥̅ appeared in the 95% confidence interval
b. µ 𝑜 appeared in the 95% confidence interval
c. µ 𝑜 did not appear in the 95% confidence interval
d. 𝑥̅ did not appear in the 95% confidence interval
13. A Type II error is made when
a. the null hypothesis is not rejected when it is false.
b. the null hypothesis is rejected when it is true.
c. the alterbative hypothesis is accepted when it is false.
d. the null hypothesis is accepted when it is true.
14. Which of the following values of Pearson’s correlation coefficient indicates the weakest
relationship?
a. 0 b. 0.8 c. -0.9 d. 0.1
15. A population consists of 8 items. The number of different simple random samples of size 3 that
can be selected from this population is:
a. 24 b. 56 c. 512 d. 128
16. 5
7
C 𝑝5(1 − 𝑝)2
is the probability of:
a. exactly two failures b. exactly two successes
c. at least two failures d. exactly five failures
17. Skewness is used a term opposite to :
a. Dispersion b. Symmetry c. Non-symmetry d. none of these
18. In a distribution which is moderately skewed to the right, mean is _____ median.
a. equal to b. greater than c. less than d. none of these
19. If 25% of values are less than 80 & 25% are more than 140, then the semi inter quartile range is:
a. 60 b. 40 c. 30 d. 70
20. Variance of 10 observations is 25, if 5 is subtracted from each observation, then variance of new
observations is:
a. 20 b. 0 c. 30 d. 25
21. The measure of variation which measures the length of interval that contains the middle 50% of
data is known as:
a. Quartile deviation b. Semi-inter quartile range
c. Inter quartile range d. none of these
22. If Y is the observed value & 𝑦̂ is the estimated value (estimated by using the regression line)
then ∑(𝑌 − 𝑌̂):
a. Should be zero b. Is likely to be close to zero
c. In majority of the cases would be equal to zero d. None of these
23. While calculating “r” if x & y are interchanged i.e instead of calculating 𝑟𝑥𝑦 if 𝑟𝑦𝑥 is calculated
then:
a. 𝑟𝑥𝑦 = 𝑟𝑦𝑥 b. 𝑟𝑥𝑦 > 𝑟𝑦𝑥 c. 𝑟𝑥𝑦 < 𝑟𝑦𝑥 d. None of these

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Faculty: AMIR KHATRI
24. If 𝑆 𝑥𝑦 = 0.6, 𝑆 𝑥 = 4.1 & 𝑆 𝑦 = 0.23 then r is equal to:
a. 0.7976 b. 0.636 c. 0.4048 d. None of these
25. The equation 1995 = 100 indicates that the index numbers are calculated using:
a. Base year 1995 b. Current year 1995
c. Previous year 1995 d. None of these
26. If the purchasing power of money is multiplied by the current per capita income the resulting
value is known as:
a. Rate of inflation b. Error in per capital income
c. Real (deflated) per capita income d. None of these
27. 3
10
P = 720 then 3
10
C =?
a. 120 b. 2,160 c. 720 d. None of these
28. Three horses A,B & C are in a race; A is twice as likely to wins as B & B is three times as likely to
wins as C. The probability that B or C wins is:
a.
3
5
b.
2
5
c.
3
10
d. None of these
29. The statement “The number of typing mistakes per page by typist“ may describe a random
variable that may possess:
a. Binomial distribution b. Poisson distribution
c. Normal distribution d. None of these
30. Random samples of size 81 are taken from an infinite population whose mean & standard
deviation are 200 & 18 respectively. The distribution of the population is unknown. The mean &
the standard error of the mean are:
a. 200 & 18 b. 81 & 18 c. 9 & 2 d. 200 & 2
31. Suppose that you are a student worker in the library & they agree to pay you using the Random
Pay System. Each week your supervisor flips a fair coin. If it comes up head, your pay for the
week is $80 & if it comes up tail your pay for the week is $40. What is the expected value of your
weekly pay?
a. $20 b. $40 c. $60 d. $80
32. If the mean of five observations x, x+2, x+4, x+6, x+8 is 11, then the mean of first three
observations is :
a. 9 b. 11 c. 13 d. none of these
33. A stem & leaf display which follows, has been used to sort 44 data values.
1 1 2
2 1 2 2 3 5
3 0 1 5 5 8 9 9
4 2 3 3 3 5 5 5 5 8 8 8 8 9
5 1 2 3 4 4 5 6
6 1 1 6 6 7 8
7 1 1 2 3
Find the median & mode for these data:

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Faculty: AMIR KHATRI
a. median = 46.5 & mode = 45
b. median = 48 & mode = 45
c. median = 45 & mode = 45, 48
d. median = 46.5 & mode = 45, 48
34. There are n socks, 3 of which are red, in a drawer. What is the value of ‘n’ if when 2 of the socks
are chosen randomly, the probability that they are both red is
1
2
?
a. 6 b. 8 c. 4 d. None of these
35. You want a 90% confidence interval for the average amount of time (in minutes) spent per week
on homework by the students of KnS. The interval is to have a margin of error of 2 minutes, &
the time spent has a normal distribution with a standard deviation 𝜎 = 30 𝑚𝑖𝑛𝑢𝑡𝑒𝑠. The
number of observations required is closest to:
a. 25 b. 30 c. 609 d. 865
36. An organization has collected the following data showing relationship between price charged &
quantities sold:
Price 5 6 7 8 9 10 12 13
Quantity 590 560 555 540 525 500 480 475
Using the above data, calculate the value of ‘a’ for the equation Y = a + bx
a. 653.25 b. -14.30 c. 668 d. None of these