Question

Below is a table published in a report by the CDC that provides estimates of flu vaccine coverage by race for all adults 19+ years in the US.

TABLE 1. Estimated proportion ofadults aged 219 years who received selected vaccinations, by age group, increased-risk status," and race/ ethnicityt-National Health Interview Survey. United States, 2015 Vaccination, age group, increased-risk status, and race/ethnicity Sample size Simple difference from 2014 (95% CI) Influenza vaccination, 2014-15 season 19 yrs Total White Black Hispanic or Latino Asian Other 31,897 19,905 4,159 5,286 1,733 814 44.8 48.5 37.7 33.0 49.0 43.0 (43.7-45.8) (47.2-49.8) (35.3-40.3)* (30.9-35.2)** (44.8-53.3) (35.5-51.4) 1.6 1.8 1.2 -0.2 4.4 4.4

A) What is the point estimate for percent of all White adults ≥ 19 years who received flu vaccine?

B) Interpret the 95% CI for the percentage of all White adults ≥ 19 who received flu vaccine in words.

C) (1)  Using the confidence interval widths and your knowledge of how CIs for population proportions are constructed, determine the margins of error (E) for Whites and for Asians and compare them.

(2)  Since both groups have similar point estimates, why is the margin of error larger for the Asian population?

Answer 1

a) the point estimate for per cent of all White adults ≥ 19 years who received flu vaccine =48.5%

b) it states that we are 95% confident that the population percentage of all White adults ≥ 19 who received flu vaccine lies within the interval (47.2 - 49.8).

c) margin of error for the whites is

the margin of error for the Asians is $\frac{53.3-44.8}{2}=4.25$

Since the sample size of the whites is higher than Asians, their margin of error is less compared to the Asians.