Question

in a nursing home study, the researchers found that 15 out of 34 randomly selected small nursing homes had a resident vaccination rate of less 80%, while 17 out of 27 randomly selected large nursing homes had a resident vaccination rate of less than 80%. at a = 0.05, test the claim that there is a lower proportion of small nursing homes with a resident vaccination rate of less than 80% than large nursing homes. let small nurising homes be population1.y

Answer 1

Solution : Given that: ni = 34 x = 15 P = 0.8 12 =27 X 2 = 17 . P2 = 0.8 P = x 2 = 4 x 2 2 15 34 = 17. 27 = 0.4412 = 0.6296 x = 0.05 Hypothesisi Hoip, = P2 Ha p <P2 Test statistic : - CP - P2) - (Pi-P2) u tti xit x2 ntn2 P = is t17 34727

P = 32 ł = 0.5246 10 lor lo 0 = 1- O = 1-0.5246 7 = 0.4754 - (0.4412-0.6296) 0.5246 *0.4754 x 34 +23) - 0.1884 0.1287 z = -1.4639 = -1.464 - P-value = 0.07 - p-value > x=0.85 so we fail to séject Ho. ... This samples not provide evidence to proove claim. - P = P2.