Question

A recent article in The Wall Street Journal reported that the home equity loan rate is now less than 4%. A sample of eight small banks in the Midwest revealed the following home equity loan rates (in percent):

3.6	4.1	5.3	3.6	4.9	4.6	5.0	4.4

At the 0.01 significance level, can we conclude that the home equity loan rate for small banks is less than 4%? Estimate the p-value.

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1. What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

2. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

3. What is your decision regarding H₀?

4. Estimate the p-value.

Answer 1

Answer)

Null hypothesis Ho : u = 4

Alternate hypothesis Ha : u < 4

First we need to find the sample mean and s.d of the given data

Mean = 4.4

S.d = 0.6

A)

As the population s.d is not given we will use t distribution to conduct the test

Degrees of freedom is = n-1 = 7

For 7 dof and 0.01 significance

We will use t distribution table to estimate the critical value t = -2.998

Rejection region is less than -2.998

So, decision rule is

Reject Ho if test statistics is less than -2.998

B)

Test statistics t = (sample mean - claimed mean)/(s.d/√n)

t = (4.4 - 4)/(0.6/√8) = 1.89

C)

Since 1.89 is not less than -2.998

we fail to reject Ho

D)

For 1.89 test statistics and 7 dof

P-value from t distribution is = 0.949662