lecture 2 mcqs part 2

Question 1

1. Which of the following is not a characteristic of a normal distribution?
   A) Symmetrical
   B) Mean equals median equals mode
   C) Discrete outcomes
   D) Most data falls close to the mean

Answer 1

c

Question 2

2. In a dataset, if the mean = 50 and standard deviation = 5, approximately 95% of values lie between:
   A) 40 and 60
   B) 45 and 55
   C) 35 and 65
   D) 30 and 70

Answer 2

C

Question 3

3. A histogram is bell-shaped and symmetrical. Which distribution is most likely?
   A) Poisson
   B) Normal
   C) Binomial
   D) Exponential

Answer 3

B

Question 4

4. A dataset has mean = 20, median = 15, mode = 12. What is the likely shape?
   A) Symmetric
   B) Right-skewed
   C) Left-skewed
   D) Uniform

Answer 4

B

Question 5

5. Which summary statistic is least affected by outliers?
   A) Mean
   B) Mode
   C) Standard deviation
   D) Median

Answer 5

D

Question 6

6. What is the range of a theoretical normal distribution?
   A) Between 0 and 100
   B) Between -3 and +3
   C) Infinite
   D) Between 1st and 3rd quartile

Answer 6

C

Question 7

7. What is the first step in assessing normality of your data?
   A) Run a t-test
   B) Plot a histogram
   C) Calculate variance
   D) Apply a linear regression

Answer 7

B

Question 8

8. Which of the following would suggest data are NOT normally distributed?
   A) Bell-shaped histogram
   B) Mean ≈ Median
   C) Kolmogorov-Smirnov test p < 0.05
   D) Q-Q plot points forming a straight line

Answer 8

C

Question 9

9. In a Q-Q plot, a strong deviation from the diagonal line suggests:
   A) Normality
   B) Non-normality
   C) Constant variance
   D) Equal means

Answer 9

B

Question 10

10. What does the standard error quantify?
    A) Spread of the population
    B) Bias in sampling
    C) Variability of the sample mean across samples
    D) Deviation of a single data point from the mean

Answer 10

C

Question 11

11. Which of the following reduces standard error?
    A) Increasing variability
    B) Decreasing sample size
    C) Increasing sample size
    D) Increasing standard deviation

Answer 11

C

Question 12

12. If 75% of observations lie within 1 standard deviation of the mean, what does that suggest?
    A) More variable than a normal distribution
    B) Less variable than normal
    C) Normal
    D) Uniform

Answer 12

A

Question 13

13. The standard error (SE) of the mean is calculated as:
    A) SD / n
    B) SD × √n
    C) SD / √n
    D) √(SD)

Answer 13

C

Question 14

14. In statistical inference, what is the main role of confidence intervals?
    A) To identify outliers
    B) To estimate the p-value
    C) To express uncertainty in an estimate
    D) To test causality

Answer 14

C

Question 15

15. A small sample has mean = 10, SD = 2, n = 4. What is the standard error?
    A) 0.5
    B) 1.0
    C) 1.41
    D) 2.0

Answer 15

B

Question 16

16. Which test checks if a dataset is normally distributed?
    A) Paired t-test
    B) Chi-squared test
    C) Kolmogorov-Smirnov test
    D) ANOVA

Answer 16

C

Question 17

17. What is sampling variation?
    A) Data entry error
    B) Change in population mean
    C) Differences in sample statistics due to chance
    D) Variability from bias

Answer 17

C

Question 18

18. In Lecture 2, coffee consumption showed mean ± SD = 8.1 ± 9.7. What % of observations fell within 1 SD?
    A) 68%
    B) 75%
    C) 90%
    D) 95%

Answer 18

C

Question 19

19. What is a statistic, in the context of inference?
    A) A known population parameter
    B) A number describing a sample
    C) A p-value
    D) A model assumption

Answer 19

B

Question 20

20. If a dataset’s mean = median = mode, the distribution is:
    A) Right-skewed
    B) Left-skewed
    C) Uniform
    D) Symmetric

Answer 20

D

Question 21

21. Which of the following statements about the standard deviation (SD) is true?
    A) It describes the spread of individual values in a sample
    B) It decreases as sample size increases
    C) It measures variability of sample means
    D) It estimates the population mean

Answer 21

a

Question 22

22. What is the difference between standard deviation and standard error?
    A) SD describes population spread; SE describes sample spread
    B) SD measures spread of data; SE measures spread of sample means
    C) SE is always larger than SD
    D) They are mathematically identical

Answer 22

B

Question 23

23. What does the central limit theorem state?
    A) Larger samples produce higher standard deviations
    B) The population distribution must be normal
    C) Sampling distributions of the mean approach normality as n increases
    D) Mean = mode = median in all datasets

Answer 23

C

Question 24

24. Which of the following would not indicate non-normality?
    A) A symmetric histogram
    B) Skewed boxplot
    C) Shapiro-Wilk p < 0.05
    D) Q-Q plot points curving away from diagonal

Answer 24

A

Question 25

25. Which tool is used to visualise normality most directly? A) Boxplot B) Scatterplot C) Q-Q plot D) Bar chart

Answer 25

C

Question 26

26. What is a common rule of thumb for the proportion of observations within 2 SDs in a normal distribution? A) 50% B) 68% C) 95% D) 99.7%

Answer 26

C

Question 27

27. If the standard deviation is large, the data are: A) Closely clustered around the mean B) More spread out C) Uniform D) Normally distributed

Answer 27

B

Question 28

28. The mean is most appropriate as a summary measure when: A) The data are skewed B) There are many outliers C) The data are symmetrical and continuous D) The variable is categorical

Answer 28

C

Question 29

29. What is the purpose of statistical inference? A) To describe the population using sample data B) To calculate the median C) To plot the data D) To reduce sample size

Answer 29

A

Question 30

30. If a sample mean is 12 and SE is 2, what is the 95% confidence interval approximately? A) 8 to 16 B) 10 to 14 C) 11 to 13 D) 6 to 18

Answer 30

B

Question 31

31. The mean ± 2 SE rule helps approximate: A) Confidence intervals B) Medians C) P-values D) Sample size

Answer 31

A

Question 32

32. A boxplot displays which features of data? A) Mean, mode, and SD B) Minimum, quartiles, and maximum C) Histogram frequency D) Normality

Answer 32

B

Question 33

33. In a sample of 100, which will be smaller: A) Standard error B) Standard deviation C) The mean D) The range

Answer 33

A

Question 34

34. Why do researchers use samples instead of entire populations? A) Populations are always biased B) Statistical tests don’t work on populations C) Sampling is more practical and efficient D) Samples are more accurate

Answer 34

A

Question 35

35. Which of the following describes sampling distribution? A) Distribution of data in the population B) Distribution of a statistic (like the mean) from repeated samples C) Distribution of the confidence interval D) Distribution of errors in measurement

Answer 35

B

Question 36

36. What is the main assumption behind using a sample to estimate the population? A) The sample is biased B) The sample is randomly selected and representative C) The population is always normal D) The standard deviation is known

Answer 36

B

Question 37

37. The mean of sample means from repeated sampling equals: A) 0 B) Median of population C) Sample standard error D) Population mean

Answer 37

D

Question 38

38. A symmetrical boxplot suggests: A) A categorical variable B) A uniform distribution C) A roughly normal distribution D) A skewed distribution

Answer 38

C

Question 39

39. Which method would be least useful in assessing normality? A) Q-Q plot B) Boxplot C) Histogram D) Bar chart

Answer 39

D

Question 40

40. A small standard error implies: A) Greater variability across samples B) A biased estimator C) More precise estimate of the population mean D) The data are skewed

Answer 40

C