Question 7.173

image 47. Facebook Accounts. Refer to Exercises 42 and 46. What if we increased the sample size to some unspecified larger number? Describe how and why the following quantities would change, if at all:

  6. 2.5th percentile of the sample proportions
  7. 97.5th percentile of the sample proportions

7.2.47

(a) Remains the same since does not depend on .

(b) Decrease. Since the sample size is in the denominator of decreases as the sample size increases. (c) Decrease. Standardizing we get . From (b), decreases as the sample size increases. Therefore increases as the sample size increases. Therefore decreases.

(d) Increase. Standardizing we get and . From (b), decreases as the sample size increases. Therefore decreases and increases as the sample size increases. Thus increases as the sample size increases. (e) Decrease. Standardizing we get . From (b), decreases as the sample size increases. Therefore decreases as the sample size increases. Thus decreases as the sample size increases. (f) Increase. The 2.5th percentile is found by the formula . From (a) remains the same as the sample size increases and from (b) decreases as the sample size increases. Therefore increases as the sample size increases. (g) Decrease. The 97.5th percentile is found by the formula . From (a) remains the same as the sample size increases and from (b), decreases as the sample size increases. Therefore decreases as the sample size increases.