41. The median of a set of 75 observations was calculated as 29. It was later discovered that one observation was wrongly read as 43 instead of correct value 53. The correct value of the median is:

(a) 29

(b) 39

(c) 43

(d) 53

(a) 29

(b) 39

(c) 43

(d) 53

**Answer: (a)**

42. From a population of 6 individuals one has to draw a simple random sample of size 2 without replacement. What is the number of possible samples that can be drawn?

(a) 36

(b) 12

(c) 15

(d) 4

(a) 36

(b) 12

(c) 15

(d) 4

**Answer: (c)**

43. Consider the following statements regarding arithmetic mean and median of a positively skewed distribution:

1. If the mean is 45, then the median cannot be 50.

2. The mean absolute deviation is the least when computed from the mean.

3. If the largest value in the distribution is increased by 5, then the median also increases by 5.

1. If the mean is 45, then the median cannot be 50.

2. The mean absolute deviation is the least when computed from the mean.

3. If the largest value in the distribution is increased by 5, then the median also increases by 5.

Which of the above statements is/are correct?

(a) 1 only

(b) 1 and 2

(c) 2 only

(d) 3 only

(a) 1 only

(b) 1 and 2

(c) 2 only

(d) 3 only

**Answer: (a)**

44. Two independent groups of 6 children were tested to find out how many words they could repeat from memory after hearing 10 words. The results were as follows:

The most appropriate test that should be applied to test whether there is any significant difference between the average performance of the two groups A and B is:

(a) Z‐test

(b) Two sample t‐test

(c) Paired t‐test

(d) Chi square test

(a) Z‐test

(b) Two sample t‐test

(c) Paired t‐test

(d) Chi square test

**Answer: (b)**

45.

(a) 2

(b) 3

(c) 4

(d) 5

(b) 3

(c) 4

(d) 5

**Answer: (b)**

46. For an optimum allocation in stratified sampling, consider the following statements:

1. In a stratum, a larger sample is selected if the stratum is larger.

2. A smaller sample is selected from a stratum if the stratum is less variable internally.

1. In a stratum, a larger sample is selected if the stratum is larger.

2. A smaller sample is selected from a stratum if the stratum is less variable internally.

Which of above statements is/are correct?

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

**Answer: (c)**

47. The standard deviation of the waiting time of the 25 persons waiting in an ATM queue was found to be 4 hours. The standard error of the estimator of the population mean for a simple random sample with replacement of size 25 persons will be:

(a) 48 minutes

(b) 60 minutes

(c) 9.6 minutes

(d) 40 minutes

(a) 48 minutes

(b) 60 minutes

(c) 9.6 minutes

(d) 40 minutes

**Answer: (a)**

48. For 2000 patients, a simple random sample of 400 patients was selected. Out of these selected patients, 80 patients responded to a particular drug. The standard error of the proportion of the responded patients will be:

(a) 0.16

(b) 0.02

(c) 0.50

(d) 0.40

(a) 0.16

(b) 0.02

(c) 0.50

(d) 0.40

**Answer: (b)**

49. For estimating the population proportion P in a class of a population having 500 units, the variance of the estimator p of P based on sample size 50 is:

(a) 10PQ/499

(b) PQ/499

(c) 9PQ/499

(d) 499PQ/22500

(a) 10PQ/499

(b) PQ/499

(c) 9PQ/499

(d) 499PQ/22500

**Answer: (c)**

50. From a population of size 5, the total number of possible sample of size 3 using Simple Random Sample With Replacement is:

(a) 15

(b) 60

(c) 279

(d) 125

(a) 15

(b) 60

(c) 279

(d) 125

**Answer: (d)**

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