Question

Recently the national average yield on municipal bonds has been µ = 4.19%. A random sample of 16 Arizona municipal bonds had an average yield of 5.11% with a sample standard deviation of s = 1.15%. Does this indicate that the population mean yield for all Arizona municipal bonds is greater than the national average? Use a 5% level of significance. Assume x is normally distributed.

(A) State the null and alternate hypotheses and the level of significance. Is the test left-tailed, right-tailed, or two-tailed?

(B) Identify the appropriate sampling distribution: the standard normal or the Student’s t.

(C) What is the value of the sample test statistic?

(D) Find or estimate the P-value.

(E) Based on your answers for parts (a) through (d), will you reject or fail to reject the null hypothesis?

Answer 1

Solution-A:

Null hypothesis:

Ho: µ = 4.19%

Alternative Hypothesis:

Ha: µ > 4.19%

its right-tailed

(B) Identify the appropriate sampling distribution: the standard normal or the Student’s t

Since population standard deviation is not given  

n=16,so use t distribution

(C) What is the value of the sample test statistic?

t=xbar-mu/s/sqrt(n)

=(5.11-4.19)/(1.15/sqrt(16))

t =3.2

(D) Find or estimate the P-value.

df=n-1=16-1=15

p value in excel is

=T.DIST.RT(3.2;15)

=0.002981924

p=0.0029

(E) Based on your answers for parts (a) through (d), will you reject or fail to reject the null hypothesis?

p<0.05

Reject null hypothesis