mean weight X 170 pounds and S2 mean weight X 170 pounds an

mean weight X = 170 (pounds) and S2 mean weight X 170 (pounds) and s2 250. Find the prob-value for and test the hypothesis Ho: = 180 H1:

H0: mu=180 vs H1: mu<180

level of significance 0.05

sample size=n=20 sample mean=xbar=170 sample SD=s=sqrt(250)=15.81

the test statistic is T=sqrt(n)*(xbar-mu)/s which under H0 follows a t distribution with df n-1=20

now observed value of T is t=sqrt(20)*(170-180)/15.81=-2.8286

hence prob value is p=P[T<-2.8286] where T follows a t distribution with df n-1=20

p=0.0053664 [answer]

so p<0.05 hence we reject the null hypothesis and conclude on the basis of the given data at hand that mu<180 [answer]