Answer Happy

can use R to solve the standard normal probability
A pharmaceutical company - AstroZomoro, develops a vaccine against Covid-19. It is required to show statistical evidence for the efficacy of its vaccine. Under the null hypothesis, suppose we believe that vaccinated people have a 1% probability of being infected within a year after vaccination. AstroZomoro wishes to collect evidence that its new vaccine is highly protective, in the sense that the proportion of vaccinated people who become infected within a year of being vaccinated is lower than 1%. Suppose n people are enrolled in a trial, where n is reasonably large. (i) Terangkan bagaimana kita dapat menggunakan ujian-Z untuk perkadaran tunggal bagi menguji hipotesis nol di atas pada aras keertian 1%. Explain how we can use the Z-test for single proportion to test the above null hypothesis at a 1% level of significance. (ii) Di bawah hipotesis alternatif bahawa hanya 0.1% daripada orang yang diberikan vaksin akan dijangkiti dalam masa setahun selepas pemvaksinan, apakah bilangan minimum orang yang layak yang harus didaftarkan dalam ujian tersebut supaya ujian-Z untuk perkadaran tunggal mempunyai kuasa 80% untuk mengesan hipotesis alternatif ini? Under the alternative hypothesis that only 0.1% of vaccinated people will be infected within a year after vaccination, what is the minimum number of eligible people that should be enrolled in the trial in order part (i) to their own data. What outcomes would they obtain?