A French research team claims that patients undergoing a spe

A French research team claims that patients undergoing a specific cancer treatment have an 85% five-year survival rate. The same treatment is tested in the United States, and 48 out of 60 patients survive five years. Test the hypothesis that the US study has the same survival rate claimed by the French. Use a two-sided test at the 5% level of significance. show work

Solution

The test hypothesis:

Ho: p=0.85 (i.e. null hypothesis)

Ha: p not equal to 0.85 (i.e alternative hypothesis)

The test statistic is

Z=(phat-p)/sqrt(p*(1-p)/n)

=(48/60-0.85)/sqrt(0.85*0.15/60)

=-1.08

Given a=0.05, the critical values are Z(0.025) = -1.96 or 1.96 (from standard normal table)

The rejection regions are if Z<-1.96 or Z>1.96, we reject Ho.

Since Z=-1.08 is between -1.96 and 1.96, we do not reject Ho.

So we can conclude that the US study has the same survival rate claimed by the French.