Question

To test H₀: mean = 20 vs H₁: mean < 20 a simple random sample of size n = 18 is obtained from a population that Is known to be normally distributed

(a) If x-hat = 18.3 and s = 4.3, compute the test statistic

(b) Draw a t-distribution with the area that represents the P-value shaded

(c) Approximate and interpret the P-value

(d) If the researcher decides to test this hypothesis at the a = 0.05 level of significance, will the researcher reject the null hypothesis? Why?

Answer 1

Solution:

Part a

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 20

Xbar = 18.3

S = 4.3

n = 18

t = (18.3 – 20)/[4.3/sqrt(18)]

t = -1.6773

Test statistic = -1.6773

Part b

The P-value by using t-curve is shown below:

Part c

We have

n = 18

df = n- 1 = 17

t = -1.6773

Test is lower tailed test.

So, P-value by using t-table is given as below:

P-value = 0.0559

This is the maximum significance level at which we reject the null hypothesis.

Part d

P-value > α = 0.05, so we do not reject the null hypothesis.

Researcher does not reject the null hypothesis because P-value is greater than given level of significance.