Question

as of july 16, 2020 Wilsonville had tested 21,641 people for COVID, 1,975 of those tested were positive indicating that they were infected.

construct a 92 percent confidence interval for the true proportion, p, of tested residents in Wilsonville that are infected with the virus. List the margin of error.

on July 16, 2020 it was also reported that 9,756 people in Lincoln had been tested and 438 were shown to be infected. Is the rate of infection in Wilsonville significantly different from the infection rate for Lincoln? Explain your reasoning

Answer 1

Let 1975 x= People those tested were positive indicating that they were infected, nie sample size = 21.641 people who infected among the in Wilson will proprotion of 21 641 1975 O 0913 21641 ni Now for we know loo (1-2)% confidence interval true proportion p is Zd/2 له لكم P + 242 Vaclip ni Here we have to find 92% confidence interval for then true proportion P Z 62 Zo.08 = 20.04= 1.75 2 lower bound for P. Zotz Pi (I-P ni O. 0913 (1.75x 0.0913(1-00913) 21 641 ! 0.0879 Upper bound for pi + Zatz C. Pi (1) (1.75 = 0.0913+ (1.25 X 0.0913 (1-00913) 21641 0.0 947 CS Scanned with CamScannen

DATE 92% confidence interval for true proportion (0:0879 0.0947) is Now X2 = Number of people to be infected in the Lincoln 438 m2 = sample size 9756 P2 = proportion of people to be infected in the sample 9756 IT 0.0449 Nz 438 9756 Now P Ê = nipi +12 p2 nitha (21641% 0.0913)+(9756% 0.0449) 21641 +9756 U 0.0769 Ô = (1-P) (1-0.0769) = 0.923) Let Piz Proportion of infected people in Wilsonville P2 = proportion of infected people in Lincoln Here we have to test Ho: Pi=P2 i e, There is no significant difference in proportion in wilsonville and Lincoln Hi Pitpz le There is significand difference in proportion in Wilsonville and Lincoln. CS Scanned with CamScanner

Under Ho the test statistic is z = pip Ñ Ô N(0, 1) (for large n, and nz) Itt ni 12 0.0913-00449 0:0769 X 0923) X ( 21641 9756 Z 14.2811 Tabulated value value at 20/2 = Zo.08 E 2004 is 1.75 2 we Conclusion - Since Izl > 1.75 reject Ho at 8% level of significance and conclude that there is significant difference in proportion in wilsonville and lincoln CS Scanned with CamScanner