You are given the following information obtained from a rand

Solution

here sample mean=Xbar=19     sample SD=S=2      sample size=n=5

here null hypothesis H0=population mean=mu=21         and alternative hypothesis H1=population mean=mu<21

here alpha=0.10

test statistic is T=(Xbar-mu)*sqrt(n)/s which under H0 follows a t distribution with degrees of freedom 5-1=4

so we reject h0 iff observed value of T=t<t_4,alpha=0.1   where t_4,alpha=0.1 is the upper 0.1 point of a t distribution with 4 degrees of freedom

now observed value of t is (19-21)*sqrt(5)/2=-2.236

and t_4,alpha=0.1=1.53321

so -2.236<1.53321

hence we reject H0 and conclude that the mean of the population from which this sample was taken is significantly less than 21.