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. If we assume that the population proportions for young adults and middle-age adults are the same, so p1 = P2, would the samples we observed be unusual? Select the appropriate option below. Yes, since the Z-score of the difference in sample proportions is less than 2. Yes, since the Z-score of the difference in sample proportions is greater than 2. O No, since the Z-score of the difference in sample proportions is greater than 2. O We can't determine whether these sample results are unusual.

Answer 1

X = 33 Let X 2 be di and adults Let xi be the number of young adults concerned about the economic impact of the virus, but not the health impact sample size, n = 100 number of middle-age adults concerned about the economic impact of the virus, but not the health impact, x2 = 22, sample size n₂ = 110 Now, let &, and he be the sample proportion and $2 be the population proportion of young and middle adults respectively 33 -0.33 = 22 the Hypothests, Hi bi tb₂ Hi: pi-P2 &0. Test statistic (A - 2) - (P. -P2) where i = xptar nith È (1-6) (+ 1 - 2 ) Now Ho: b = P2 Ho: Pi-b2 = 0 vs. vs. Z = 33 +22 110+100 0.262 under Ho, Z = O ✓ Å (1-6) ( 2 + 1 22 ) (0.33 -0.2) 0.262 ( 1-0.262) (trotto) = 2:139 -0.01 Now, at 1 % level of significance, we get the value of zo = 2.58 from z-value Table If z 7 28.01 = 2.58 we reject the null hypothesis otherwise we aceept it. * $2.58 we accept the Here Z = 2.139 Loor null ie the sample we hypothesis Ho: P, = 62 observed not unusual. Therefore answer is - No, since the z-score of the difference in sample proportion is greater than 2. were