Question

4.14 Biologists are studying the weights of 13-year-old American girls. They are confident that the population is normally distributed and that µ equals 85 pounds, but they are interested in the population variance σ2 and would like to do a hypothesis test. They want to know if σ2 = 75 pounds and suspect that the actual value may be greater than this. A random sample of 19 girls has a sample variance of s2 = 150 pounds. Report H0, Ha, the rejection region (use α = .05), test statistic, conclusion, and place bounds on the p-value.

Answer 1

Ho:       σ2	=	75
Ha:        σ2	>	75

degree of freedom =n-1=19-1=18

for 5 % level and given df critical values of X2 =			28.869
Decision rule:reject Ho if test statistic X2			>28.869

test statistic X2 =(n-1)s2/ σ2=(19-1)*150/75 =

36.00

since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that population variance is greater than 75

bound on p value : 0.005 <p value <0.01