Question

I need help with 8.45 but youll need 8.38 for that

8.45 Sample size for coffee. Refer to Exercise 8.38 where we analyzed data from a matched pairs study that compared preferences for instant versus fresh-brewed coffee. Suppose that you want to design a similar study. The null hypothesis is that instant and fresh-brewed are equally likely to be preferred and the alternative is two- sided. You will use a = 0.05. What is the sample needed to detect a preference of 60% for fre with 0.80 probability? nce of 60% for fresh-brewed

Answer 1

Solution: (S.38) Given hat Sleay2prek the instent Coffee and emaining 29 peferel fesh go Subjects uoho participated n the brewed coffee The proporton of Subjects uoho preteedl fesh byewed Coffee 39 60 -o65 P-065 a) Tt is to ohether majority of people be tested fresh breuwed Coffee or not Preter the taste af who prefer fresh-brewd Hohe poportion ot people coffe 's o. 5 - P 0.5 HThe Proporton of Major y of People pvefer of fresh-lovewed Coffe p >o.5 taste To test he above hypothe Sisthe -StafiStic is

O.65-0.5 60 O.I5 O.25 O.15 O o04166 0.0645497 2.3237908 PZ> 2.32) The p-value of the ven dest 6rigt taild 1-P(z 2-3) |- O.q 8982959 Efoom 2table) P-vakue Oolo1104 (b Standand Nlormal curve. -X 2.32 2.32

less han -the tnificance leel, the p-value s d 0.05 rutt hypotheris. we rejott the Thee is enough euiden le to upport the people p ter the tate that major of Loffee claim Avesh breuced of