STA301 Most Repeated Subjective Questions Jan 2025 by Usama Farooq

STA301 – Statistics and Probability

1. Explain Null and alternaƟve hypothesis.

Q2. RelaƟon between criƟcal region and tesƟng?

Q3. AthemaƟc mean uses?

Q4. Mean deviaƟon for ungroup data was given?

Q5. Coefficient of variaƟons?

Q6. First two moments?

7. P(A/B) and P(B/A)? Values was given
8. In least square regression line, X is a NON-RANDOM variable, whereas Y is a RANDOM variable. For example, consider the case of agricultural experiments.
9. A hypotheƟcal populaƟon can be defined as the aggregate of all the conceivable ways in which a specified event can happen.
10. QuanƟtaƟve variable

Q11. Which is not dispersion?

Q12. Census is primary data or secondary data?

13. John Tukey (1977)
14. Describe the Stem-and-Leaf Display.

Q15. Right-skewed distribuƟons?

16. The posiƟvely skewed curve
17. CondiƟonal probability of the event B given that event A has occurred, wriƩen as P(B/A), is defined by
18. Median of -3, 3, 5,6,7,10,11 is

Q19. If a data of 20 values, all are 5 then arithmeƟc mean is?

20. Which is not measure of central tendency

Q21. CommutaƟve frequency distribuƟon is also known as?

22. Law equaƟons
23. Linear regression line

Q24. Y=a=bx in this equaƟon b constat represent?

Q25. How to find the median?

26. Cartesian product definiƟon and 2 sets where are also given there
27. Draw a polygon of the given data

Q28. Find the first 2 moments from the mean of the given data?

Q29. What is BCR?

Q30. What is hypergeometric?

Q31. How to find Union & IntersecƟon?

32. When P and N given, fine mean and standard deviaƟon.

Q33. Binomial distribuƟon?

Q34. How many black card, diamond card, heart card, face card, queen card?

35. ConƟnuous random topic (integraƟon).

Q36. What is T-distribuƟon?

37. Interval scale and raƟo scale with examples.
38. Describe Playing cards.
39. Define Stem leaf.

Q40. Binomial experiment properƟes?

Q41. Anova table?

Q42. Binomial distribuƟon?

Q43. How to find mean?

44. Find Cov(x,y) if values given.

Q45. How to independent prove X and Y if values given?

Q46. P1, N1, P2, N2 values given, find populaƟon proporƟon?

Q47. Null and alternaƟve hypothesis given, find C.R?

Q48. Confidence interval, S square and N values given, find interval of sigma square?

Q49. What about to Z distribuƟon?

Q50. Poisson distribuƟon?

51. Mean of Hypergeometric distribuƟon
52. Normal distribuƟon (high priority)
53. Binomial distribuƟon
54. Chi distribuƟon (high priority)
55. Sampling
56. TesƟng hypothesis
57. Confidence interval
58. Degree of freedom
59. F-distribuƟon, t-test, z-test, f-test
60. Formula of z test
61. Formula n sample without replacement

Q62. DefiniƟon of StaƟsƟcs?

Q63. DefiniƟon of Probability?

64. Hypothesis by z test
65. EsƟmaƟon
66. FerƟle deviaƟon
67. CriƟcal region
68. Sample distribuƟon of sample mean
69. A table given, in which x or p(x) values given, find mean and variance? E(x) and var
70. ExhausƟve event

Q71. Sampling errors?

Q72. Parameters of F distribuƟon?

Q73. How to find ArithmeƟc mean?

74. How to find Mean or variance

Q75. ProperƟes of hypergeometric?

76. Construct polygon
77. Find e3x+1
78. Find confident limit

Q79. Find coefficient of variance?

80. Suppose X is a variable between integers 1 to 14, what is the probability of X to b even number? (quesƟon like this)

Q81. About combinaƟon?

Q82. What is the probability of commiƫng to be distributed among 10 persons?

Q83. What are the different measures of dispersion that don’t use all values?

Q84. What are the two suits that can be black in playing cards?

Answers:

1. Explain Null and AlternaƟve Hypothesis

o Null Hypothesis (H₀): A statement assuming no effect or difference exists. For example, H0:μ=50H₀: \mu = 50 means the populaƟon mean is 50. o AlternaƟve Hypothesis (H₁): Opposes H0H₀, suggesƟng an effect or difference exists. For example, H1:μ≠50H₁: \mu \neq 50.

2. RelaƟon Between CriƟcal Region and TesƟng

o The criƟcal region is the range of test staƟsƟc values where the null hypothesis is rejected. It depends on the significance level (α), such as 0.05. If the calculated staƟsƟc lies in the criƟcal region, we reject H0H₀.

3. ArithmeƟc Mean Uses

o The arithmeƟc mean represents the central value of data. It is used to compare datasets and is widely applied in economics, research, and educaƟon. It is sensiƟve to outliers.

4. Mean DeviaƟon for Ungrouped Data

o Formula: Mean DeviaƟon=∑∣x−x‾∣n\text{Mean DeviaƟon} = \frac{\sum |x - \overline{x}|}{n} xx = data points, x‾\overline{x} = mean, nn = number of observaƟons. It measures the average distance between each data value and the mean.

5. Coefficient of VariaƟon (C.V.)

o Formula: C.V.=Standard DeviaƟonMean×100C.V. = \frac{\text{Standard DeviaƟon}}{\text{Mean}} \Ɵmes 100 It compares the variability of datasets with different units or means. Higher C.V.C.V. indicates greater relaƟve dispersion.

6. First Two Moments

o First Moment: Mean of the dataset, represenƟng the central locaƟon. o Second Moment: Variance, measuring data spread. Formula: Variance=∑(x−x‾)2n\text{Variance}

7. P(A|B) and P(B|A)

o CondiƟonal Probability Formula: P(A∣B)=P(A∩B)P(B), P(B∣A)=P(A∩B)P(A)P(A|B) = \frac{P(A \cap B)}{P(B)}, \, P(B|A) = \frac{P(A \cap B)}{P(A)} These values depend on the specific probabiliƟes provided.

8. Least Square Regression Line

o In regression, XX is non-random (independent variable) while YY is random (dependent variable). For example, in agricultural experiments, crop yield (YY) depends on ferƟlizer amount (XX).

9. HypotheƟcal PopulaƟon

o A populaƟon of all conceivable outcomes of an event, e.g., all possible outcomes of rolling a die infinitely.

10. QuanƟtaƟve Variable

Variables measured numerically, like age, weight, or income.

Q11. Which is Not Dispersion?

Central tendency measures like mean and median are not measures of dispersion.

Q12. Census: Primary or Secondary Data?

Census data is primary data, as it involves direct collecƟon.

13. John Tukey (1977)

Introduced exploratory data analysis techniques, like the box plot.

14. Stem-and-Leaf Display

A method to organize numerical data. The "stem" represents the leading digit(s), and the "leaf" represents the trailing digit(s).

15. Right-Skewed DistribuƟons

Most data points lie on the leŌ, and the tail extends to the right. The mean is greater than the median.

16. PosiƟvely Skewed Curve

Similar to a right-skewed distribuƟon, indicaƟng data concentraƟon towards the lower end.

17. CondiƟonal Probability P(B|A)

Defined as: P(B∣A)=P(A∩B)P(A)P(B|A) = \frac{P(A \cap B)}{P(A)}

18. Median of -3, 3, 5, 6, 7, 10, 11

Arrange: -3, 3, 5, 6, 7, 10, 11. Median = middle value = 6.

Q19. If All 20 Values Are 5, ArithmeƟc Mean?

Mean = ∑xn=20×520=5\frac{\sum x}{n} = \frac{20 \Ɵmes 5}{20} = 5.

Q20. Which Is Not a Measure of Central Tendency?

Measures of central tendency include mean, median, and mode. Standard deviaƟon is not.

21. CumulaƟve Frequency DistribuƟon

Also known as ogive.

22. Law EquaƟons Probability laws: addiƟon, mulƟplicaƟon, and Bayes’ theorem.