Question

In April 2020, many U.S. adults were concerned about the impact that the coronavirus would have on their health and financial situation. Some people were only concerned about the economic or health impact, and some people were concerned with both. Researchers decided to investigate whether adults’ perceptions of the threat of the virus varied based on their age group (younger 18 – 29 versus middle-age 40-59).

The researcher found that in a random sample of 100 young adults, 33 were concerned about the economic impact of the virus, but not the health impact. In a random sample of 110 middle-age adults, 22 were concerned about the economic impact of the virus, but not the health impact.

What is the difference in sample proportions? Round the difference to two decimal places.

The difference should be: sample proportion of younger adults who are only concerned about the economic impact minus the sample proportion of middle-age adults who are only concerned about the economic impact.

Answer 1

Solution :

Sample proportion of young adults, who were concerned about the economic impact of the virus, but not the health impact is given by,

$\large \hat{p}_{1} = \frac{33}{100} = 0.33$

Sample proportion of middle-age-adults adults, who were concerned about the economic impact of the virus, but not the health impact is given by,

$\large \hat{p}_{2} = \frac{22}{110} = 0.20$

Hence, the difference in sample proportion is given by,

$\large (\hat{p}_{1}-\hat{p}_{2}) = (0.33 - 0.20) = 0.13$

The difference in sample proportions is 0.13.

Please rate the answer. Thank you.