Question

I have a statistics multiple choice question.

Thank you

Answer 1

here Let X be the Random Variable denoting the dividend yield of Australian bank stocks.

Here X~N(a,b^2) where b is known and b=2.2.

Here we wish to test H0:a=6.4 vs H1: a>6.4.

Here we draw a sample of 13 data points X1,X2,...., X13 with mean 6.63.

Here our test statistic is 13^0.5( X(bar) - a)/b where X(bar)=6.63. a under H0 is 6.4

So the value of the test statistic is 13^0.5(6.63-6.4)/2.2=0.38.

Now the p value is P(Z>0.38)=0.352.(obtained from Normal tables.)

Since the level of significance is 0.1, we accept H0. Hence C is true.