Question

Q17. To avoid panic, it is advertised by NYC authority that only 4.5% of health workers are

          infected while on duty for COVID-19. To estimate the advertised proportion, a random sample

          of 150 health workers was selected and 3 of them were tested positive. Confidence interval (CI)

          estimate using CI=p ± Z_α/2 √p(1-p)n was calculated. Choosing α (alpha) = 0.01, underscore the

          correct statement (s) from the following:

          a. CI estimates and Z_STAT to test hypothesis H₀: π=0.045 vs π ≠ 0.045 give same decision                

          b. π=0.045 can be used for calculating best CI estimates

         c. CI provides more than 5% estimates of infected workers        

         d. insufficient data to provide evidence to support NYC advertisement

Answer 1

Answer:

Given,

Here at 0.01 significance level, z value is 2.576

sample proportion p^ = x/n = 3/150 = 0.02

99% CI = p +/- z*sqrt(p(1-p)/n)

substitute values

= 0.02 +/- 2.576*sqrt(0.02(1-0.02)/150)

= 0.02 +/- 0.02945

= (-0.0094 , 0.0494)

test statistic = (x - u)/sqrt(pq/n)

substitute values

= (0.02 - 0.045)/sqrt(0.045(1 - 0.045)/150)

= -1.477

Here we observe that, |z| < critical z value , so we fail to reject Ho.

So we have insufficient evidence.

i.e.,

Option A &D are right options.