STA100 Final Term Current Solved Papers

STA100 Final term Solved Paper (Spring 2020)

26/09/2020

Q1. Define Null set.

A set that contains no elements is called null set. It is denoted by {} or.

Q2. Differentiate between constant and variable with examples?

A characteristic that varies with an individual or an object is called a variable. For example, age is a variable as it varies from person to person. Constants do not change over time. Constants are simply written as numbers.

Q3. Find A+2B from following matrices?

A= 2 , B= 1

Answer: A+2B= 2 +2 1

= 2 + 2 = 4

Q4. Describe the following set builder notation: { /

50} x x N x Set of natural numbers which are less than equal to 50. It is same as {1,2,3,…,50}

Q5. Formulate the hypothesis in case of goodness of fit test.

Ho: The fit is good H1: The fit is not good.

Q6. Prove that tan

sec sin y y y 

tan sin y y = sin cos sin y y y cos y = sec y

Q7. Calculate 98% confidence interval for

and

1. 01( 1, 1) 0.01( 1, 1 1)
2. 1, 4.8, 5, 3.5 n n n n

F F S S

98% C I  0.01( 1, 1 1) 0.01( 1, 1) n n n n S S F S F S

.4.8

3. 5 5.1 3.5
4. 85
5. 5
6. 28 , 6.86

Q8. Define statistics?

That science which enables us to draw conclusions about various phenomena on the basis of real data collected on sample-basis.

Q9. Diff. b/w discrete & continuous variable.

A discrete variable is one that can take only a discrete set of integers or whole numbers. For example number of person in a family. Continuous variable can take on any value-fractional or integral within a given interval. For example weight, height, temperature etc.

Q10. Write two names of measurement scales?

1. Nominal scale
2. Ordinal or ranking scale

Q11. Differentiate b/w primary and secondary data?

Data that have been originally collected (raw data) and have not undergone any sort of statistical treatment, are called PRIMARY data. Data that have undergone any sort of treatment by statistical methods at least ONCE are called SECONDARY data.

Q12. Draw frequency polygon from the following data?

Class Frequency

(f) Mid-Point

(X)

26.95 – 29.95 28.45

29.95 – 32.95 31.45

32.95 – 35.95 34.45

35.95 – 38.95 37.45

38.95 – 41.95 40.45

41.95 – 44.95 43.45

44.95 – 47.95 46.45

Frequency Polygon

Q13. Mean=7, Median=5, Standard deviation=2 find pearson coefficient of skewness & interpret the results.

Pearson’s Coefficient of Skewness

As our answer is positive so distribution is skewed to RIGHT.

Q14. Define absolute measure of dispersion?

An absolute measure of dispersion is one that measures the dispersion in terms of the same units or in the square of units, as the units of the data.

28. 45 31.45 34.45 37.45 40.45 43.45 46.45

Frequency · Mid-points · Frequency Polygon

deviation dard tan s median mean

Q15. Write three Pythagorean identities?

cos sin

tan sec

cot sec co

Q16. Write down the significance of experimental design? (2 marks)

By an experimental design, we mean a plan used to collect the data relevant to the problem under study in such a way as to provide a basis for valid and objective inference about the stated problem. The plan usually includes:

• the selection of treatments whose effects are to be studied,
• the specification of the experimental layout, and
• the assignment of treatments to the experimental units.

All these steps are accomplished before any experiment is performed.

Q17. Write formula of range.

Q18. Write the formula of combined or pooled proportion of two samples.

Q19. Use decimal parts in each value as the leaf and rest of the digits as stem to construct the stem and leaf table for the following 10 values:

7.3, 6.1, 5.2, 3.5, 4.8, 4.6, 4.4, 4.2, 5.1, 4.9

Arrange data in ascending order: 3.5, 4.2, 4.4, 4.6, 4.8, 4.9, 5.1, 5.2, 6.1, 7.3 Stem Leaf

2,4,6,8,9 1,2

Q20. A marble is drawn at random from a box containing 10 red, 30 white, 20 blue, 15 orange. Find the probability that drawn marble is

1. Blue
2. Red

n(S)=Total marbles=75 n(Blue)=20 n(Red)=10 P(blue)=20/75 P(Red)=10/75

Q21. Range of data is 24 and no. of classes 8. Calculate class interval.

Class interval h = RANGE/No. of classes=24/8=3

Q22. Differentiate between qualitative data and quantitative data.

Quantitative data is information about quantities. It is measureable and made with instruments such as height. Qualitative data is descriptive. It is a phenomenon which can be observed but not measured such as hair color.

Q23. A fair coin is tossed 3 times. What is probability of at least 2 tails?

S=Sample space={ HHH,HTH,HHT,THH, TTH,THT, HTT, TTT } n(S)=8 Let A= at least 2 tails= { TTH,THT, HTT, TTT } P(A)=n(A)/n(S)=4/8=1/2