Lecture 2 mcqs

Question 1

. Which of the following is TRUE of a normally distributed variable?
A) Mean is always greater than the median
B) It must be based on categorical data
C) About 95% of observations fall within ±2 standard deviations
D) It has a fixed range from 0 to 100

Answer 1

C

Question 2

2. In a normal distribution of blood pressure readings (mean = 120 mmHg, SD = 10 mmHg), what range includes approximately 68% of values?
   A) 110 to 130
   B) 100 to 140
   C) 120 to 140
   D) 115 to 125

Answer 2

A

Question 3

3. A Q-Q plot for cholesterol levels is approximately linear. What conclusion is most justified?
   A) The data has extreme outliers
   B) The data is not normally distributed
   C) The data is approximately normal
   D) The standard error is zero

Answer 3

C

Question 4

4. Which of the following statements about the normal distribution is NOT correct?
   A) It is symmetrical
   B) It is used to model categorical data
   C) The mean, median, and mode are equal
   D) It has an infinite theoretical range

Answer 4

B

Question 5

5. Which test is used to formally assess normality?
   A) Chi-square test
   B) Shapiro-Wilk test
   C) t-test
   D) ANOVA

Answer 5

B

Question 6

6. A sample of 36 students has a standard deviation of 12. What is the standard error of the mean?
   A) 2
   B) 3
   C) 6
   D) 4

Answer 6

B (SE = SD / √n = 12 / √36 = 12 / 6 = 2)

Question 7

7. The standard error will DECREASE when:
   A) Sample size increases
   B) Population mean increases
   C) Standard deviation increases
   D) Data becomes more skewed

Answer 7

A

Question 8

8. In repeated sampling, what does a 95% confidence interval represent?
   A) 95% of data values lie within the interval
   B) The population mean lies in 95% of samples
   C) The method will produce an interval containing the true mean 95% of the time
   D) The interval contains 95% of standard deviations

Answer 8

C

Question 9

9. A sample of 64 people has a mean height of 170 cm with SD of 8 cm. What is a 95% confidence interval?
   A) 168 to 172
   B) 169 to 171
   C) 167 to 173
   D) 166 to 174

Answer 9

Answer: B (SE = 8/√64 = 1; CI ≈ 170 ± 2×1 = 168–172)

Question 10

10. What effect does increasing the sample size from 100 to 400 have on a 95% confidence interval for the mean?
    A) It becomes wider
    B) It remains the same
    C) It becomes narrower
    D) It becomes less accurate

Answer 10

C

Question 11

11. What is the mathematical relationship between standard error and sample size?
    A) SE = N × SD
    B) SE = SD × N
    C) SE = SD / √N
    D) SE = SD + N

Answer 11

C

Question 12

12. What is the main reason why confidence intervals are used in statistics?
    A) To determine sample size
    B) To estimate p-values
    C) To give a range of likely values for a population parameter
    D) To find outliers in a dataset

Answer 12

C

Question 13

3. A histogram of weights shows slight skewness and a mean of 80kg. Median = 77kg. What is the likely skew?
   A) Symmetric
   B) Right-skewed
   C) Left-skewed
   D) Bimodal

Answer 13

B

Question 14

14. A sample proportion is calculated from 1,000 survey respondents. Which condition justifies use of a normal approximation?
    A) Sample must be biased
    B) Sample size must be 10 or fewer
    C) np and n(1-p) > 5
    D) Standard deviation must be zero

Answer 14

C

Question 15

15. In a survey of 400 patients, 60% rated care as “excellent.” What is the standard error of this proportion?
    A) 0.02
    B) 0.04
    C) 0.03
    D) 0.05

Answer 15

Answer: C
(SE = √[p(1-p)/n] = √[0.6×0.4/400] = √0.0006 ≈ 0.0245 ≈ 0.03)

Question 16

6. In repeated surveys, the sampling distribution of the sample mean will become:
   A) Less predictable with larger samples
   B) More variable with smaller samples
   C) Non-normal
   D) Unchanged regardless of sample size

Answer 16

B

Question 17

17. Which statement about sample statistics is TRUE?
    A) They are calculated from the population
    B) They are used to estimate population parameters
    C) They remain constant across samples
    D) They are identical to p-values

Answer 17

B

Question 18

8. A study uses a 99% confidence level instead of 95%. What happens to the width of the confidence interval?
   A) It narrows
   B) It remains the same
   C) It becomes wider
   D) It equals the standard deviation

Answer 18

C

Question 19

19. Which of the following is NOT required to assume a normal distribution for sample means?
    A) Large sample size
    B) Normal distribution of population
    C) Random sampling
    D) Categorical data

Answer 19

D

Question 20

20. If a population proportion is 0.4, which sample size is sufficient to use normal approximation?
    A) 5
    B) 10
    C) 25
    D) 2

Answer 20

Answer: C
(Check np = 0.4×25 = 10; n(1-p) = 0.6×25 = 15, both >5)

Question 21

21. A dataset of reaction times is roughly bell-shaped with a mean of 250 ms and SD of 20 ms. What proportion of values fall between 230 ms and 270 ms?
    A) About 50%
    B) About 68%
    C) About 95%
    D) About 99%

Answer 21

B

Question 22

22. If the mean and median of a dataset are nearly equal, which of the following is most likely?
    A) The data is skewed
    B) The data is symmetric
    C) The data is bimodal
    D) The sample size is too small

Answer 22

B

Question 23

23. A Q-Q plot of weekly hours of TV watched shows strong deviations from the line at both ends. What is this a sign of?
    A) Perfect normality
    B) Skewness and/or outliers
    C) Homoscedasticity
    D) Equal standard errors

Answer 23

B

Question 24

24. A 90% confidence interval for exam scores is [65, 75]. What does this mean?
    A) 90% of students scored in this range
    B) 90% of the time the mean score is 70
    C) There is a 90% chance the population mean lies in this interval
    D) The interval includes 90% of the standard deviation

Answer 24

C

Question 25

25. If a 95% confidence interval is very narrow, what can you infer? A) The sample is too small B) There’s high sampling error C) The estimate is precise D) The standard deviation is large

Answer 25

C

Question 26

26. The standard error of a sample mean is influenced by: A) The number of variables measured B) The number of categories in a variable C) The standard deviation and sample size D) The number of confidence intervals

Answer 26

C

Question 27

27. A population mean is 70. Which sample mean is least likely to occur, assuming normality and a large sample? A) 71 B) 69 C) 85 D) 70

Answer 27

C

Question 28

28. When using the normal approximation for sample proportions, which condition must be satisfied? A) Sample must be under 30 B) Data must be continuous C) np and n(1–p) > 5 D) Standard error must be 0

Answer 28

C

Question 29

29. A researcher samples 25 patients, finding a mean blood glucose of 100 mg/dL and SD = 15. What is the standard error? A) 3 B) 5 C) 15 D) 0.6

Answer 29

Answer: A (SE = 15 / √25 = 15 / 5 = 3)

Question 30

30. A 95% confidence interval for average time to complete a task is (45 min, 55 min). Which of the following is FALSE? A) We are 95% confident the population mean lies between 45–55 B) It’s possible the true mean is outside the interval C) 95% of future observations will fall in this interval D) Repeating the sampling many times would include the true mean 95% of the time

Answer 30

C

Question 31

31. If a histogram shows data that is tightly clustered around the mean with small tails, we can say: A) SD is large B) SD is small C) SE is 0 D) The mean is unreliable

Answer 31

B

Question 32

32. What is the impact of a large SD on the standard error, assuming fixed sample size? A) SE decreases B) SE remains the same C) SE increases D) SE becomes negative

Answer 32

C

Question 33

33. What does the central limit theorem allow us to do? A) Assume data is normally distributed regardless of sample size B) Use normal distribution for sample means if sample size is large C) Ignore skewness in small samples D) Use median instead of mean

Answer 33

B

Question 34

34. A 99% confidence interval is calculated for two separate datasets. Compared to the 95% interval, the 99% CI will be: A) Narrower B) The same width C) Wider D) Only valid for large samples

Answer 34

C

Question 35

35. A dental school surveys 300 students and finds 72% floss daily. Which is the best point estimate of the population proportion? A) 0.50 B) 0.72 C) 1.00 D) Unknown

Answer 35

B

Question 36

36. In a sample of 100, the observed proportion with braces is 0.3. What is the standard error of this sample proportion? A) 0.045 B) 0.09 C) 0.3 D) 0.7

Answer 36

Answer: A (SE = √[0.3×0.7/100] = √0.0021 ≈ 0.045)

Question 37

37. You double your sample size. What is the effect on the standard error? A) It doubles B) It quadruples C) It is divided by √2 D) It stays the same

Answer 37

C

Question 38

38. Which of the following would make your confidence interval wider? A) Larger sample size B) Smaller standard deviation C) Switching from 95% to 99% confidence level D) Using categorical rather than continuous data

Answer 38

C

Question 39

39. What is the purpose of using confidence intervals in statistics? A) To describe the sample precisely B) To determine p-values C) To give a range where the population value likely lies D) To assess categorical frequencies

Answer 39

C

Question 40

40. If a sample is randomly drawn and large enough, the sampling distribution of the sample proportion will be: A) Skewed B) Uniform C) Approximately normal D) Unreliable

Answer 40

C

Question 41

41. A study finds that daily water intake is normally distributed with a mean of 2.5L and SD of 0.4L. What interval captures approximately 99% of intake values? A) 2.1L to 2.9L B) 1.7L to 3.3L C) 1.5L to 3.5L D) 1.3L to 3.7L

Answer 41

Answer: D (≈ mean ± 3 SD = 2.5 ± 1.2 = 1.3 to 3.7)

Question 42

42. A 95% confidence interval for mean number of hours studied is (10, 14). What can we conclude? A) The true population mean is definitely between 10 and 14 B) 95% of students study between 10 and 14 hours C) If we repeat sampling, 95% of intervals will contain the true mean D) Mean study hours for this sample was 12

Answer 42

Answer: C

Question 43

43. A researcher wants more precise estimates in future studies. What should they do? A) Reduce sample size B) Increase variability C) Increase confidence level D) Increase sample size

Answer 43

D

Question 44

44. In a normally distributed sample, which of the following is TRUE? A) The mode is usually greater than the mean B) The median lies at the point of maximum frequency C) All values fall within ±1 SD D) The mean is not representative

Answer 44

B

Question 45

45. A histogram of a variable is highly right-skewed. Which of the following is most likely? A) Mean = median B) Mean < median C) Mean > median D) SD = 0

Answer 45

C

Question 46

46. The standard deviation of a variable is 0. What does this imply? A) Data is uniformly distributed B) The mean is unreliable C) All data values are identical D) Normal distribution applies

Answer 46

C

Question 47

47. When estimating the standard error of a sample proportion, increasing the sample size will: A) Increase SE B) Decrease SE C) Have no effect D) Affect SD but not SE

Answer 47

B

Question 48

48. What is required for a confidence interval to be valid using the normal approximation? A) Data must be discrete B) The sample mean must be greater than the median C) The sample must be random and large D) The SD must be zero

Answer 48

C

Question 49

9. A researcher wants to construct a 90% confidence interval. What z-score (critical value) should they use? A) 1.64 B) 1.96 C) 2.33 D) 2.58

Answer 49

A

Question 50

50. A professor compares the test scores of two random samples (n=30 and n=100). Which will likely have the smaller standard error? A) Sample with n=30 B) Sample with n=100 C) Both will be equal D) Depends on the mean

Answer 50

B

Question 51

51. What does the standard error of the mean represent? A) The variability of data points B) The variability of sample means around the population mean C) The likelihood of Type I error D) The maximum range of a dataset

Answer 51

B

Question 52

52. A sample proportion p̂ = 0.4 is obtained from a study with n = 100. What is the standard error? A) 0.04 B) 0.05 C) 0.06 D) 0.07

Answer 52

Answer: B (SE = √[p(1-p)/n] = √[0.4×0.6/100] = √0.0024 ≈ 0.049

Question 53

53. A normal probability plot shows data points falling roughly along a straight diagonal line. What does this indicate? A) Bimodal distribution B) Heavy skewness C) Approximate normality D) High variance

Answer 53

Answer: C

Question 54

54. A confidence interval is calculated with a 5% significance level. What is the associated confidence level? A) 90% B) 95% C) 99% D) 85%

Answer 54

B

Question 55

55. The formula SE = SD / √n shows that SE: A) Is unaffected by sample size B) Increases with larger samples C) Decreases with larger samples D) Is always equal to SD

Answer 55

C

Question 56

56. The larger the confidence level (e.g. 99% vs 95%), the confidence interval will be: A) Wider B) Narrower C) Shorter D) Unchanged

Answer 56

A

Question 57

57. Which scenario satisfies the use of normal approximation for p̂ (sample proportion)? A) n=15, p=0.1 B) n=50, p=0.05 C) n=100, p=0.2 D) n=8, p=0.3

Answer 57

C (Check np = 20, n(1-p) = 80 → both >5)

Question 58

8. Which concept explains why sample statistics vary even if drawn from the same population? A) Confidence level B) Type I error C) Sampling variation D) Measurement bias

Answer 58

C

Question 59

59. What happens to a confidence interval if the standard deviation increases? A) It becomes narrower B) It becomes wider C) It remains unchanged D) It becomes more precise

Answer 59

B

Question 60

60. A 90% CI for a proportion is (0.45, 0.55). What’s the best point estimate for the population proportion? A) 0.5 B) 0.45 C) 0.55 D) Unknown

Answer 60

A