5 A recent article in The Wall Street Journal reported that

5. A recent article in The Wall Street Journal reported that the 30-year mortgage rate is now less than 6%. A sample of eight small banks in the Midwest revealed the following 30-year rates (in percent): 4.8 5.3 6.5 4.8 6.1 5.8 6.2 5.6 At 0.10 level, can you conclude that the 30-year mortgage rate is now less than 6%?

Solution

here null H0:mu=6 vs alternative H1:mu<6

we have a sample of size n=8 alpha=0.10

sample mean=Xbar(say)   and sample sd=s(say)

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

we reject H0 iff observed value of T=t<t_n-1,alpha   where t_n-1,alpha is the upper alpha point of a t distribution with degrees of freedom n-1

Xbar=5.638 s=0.635 n=8 alpha=0.1 mu=6

so t=(5.638-6)*sqrt(8)/0.635=-1.6124

and t_7,0.1=1.41492

so t<t_7,0.1

hence H0 is rejected and it is concluded based on the given data at hand is that the the 30-year mortgage rate is now less than 6%. [answer]