Paint used to paint lines on roads must reflect enough light

Paint used to paint lines on roads must reflect enough light to be clearly visible at night. Let denote the true average reflectometer reading for a new type of paint under consideration. A test of H₀: = 20 versus H_a: > 20 based on a sample of 14 observations gave t = 2.9. What conclusion is appropriate at each of the following significance levels?

(a) = .05

Reject H₀Fail to reject H₀    

(b) = .01

Reject H₀Fail to reject H₀    

(c) = .001Reject H₀Fail to reject H₀    

Solution

Since there are 14 observations in the sample so df=n-1=14-1=13. And t value is 2.9. Since alternative hypothesis suggest that test is right tailed so p-value of the test is 0.0062.

(a)

Since P-value is less than = .05 so Reject the null hypothesis.

(b)

Since P-value is less than   = .01 so Reject the null hypothesis.

(c)

Since P-value is greater than   = .001 so Fail to Reject the null hypothesis.