Question

The paint used to make lines on roads must reflect enough light to be clearly visible at night. Let µ denote the true average reflectometer reading for a new type of paint under consideration. A test of H0: µ = 20 versus Ha: µ > 20 will be based on a random sample of size n from a normal population distribution. What conclusion is appropriate in each of the following situations? (Round your P-values to three decimal places.)
(a) n = 16, t = 3.3, a = 0.05
P-value =
(b) n = 8, t = 1.8, a = 0.01
P-value =
(c) n = 26,
(d) t = -0.6

Answer 1

Answer:

(a) P-value = 0.001

Conclusion: The average reflectometer reading for the new type of paint under consideration is greater than 20.

(b) P-value = 0.036

Conclusion: The average reflectometer reading for the new paint under consideration is 20

Step-by-step explanation:

The test is a one-tailed test because the alternate hypothesis is expressed using greater than.

(a) n = 16, t = 3.3, a = 0.05

Cumulative area of the test statistic t is 0.9995

P-value = 1 - 0.9995 = 0.0005 = 0.001 (to 3 decimal place)

Conclusion:

Reject H0 because the P-value 0.001 is less than the significance level 0.05.

(b) n = 8, t = 1.8, a = 0.01

Cumulative area of the test statistic t is 0.9641

P-value = 1 - 0.9641 = 0.0359 = 0.036 (to 3 decimal places)

Conclusion:

Fail to reject H0 because the P-value 0.036 is greater than the significance level 0.01