Question

An engineer in charge of a production process that produces a stain for outdoor decks
has designed a study to test the research hypotheses that an additive to the stain will produce
an increase in the ability of the stain to resist water absorption. The mean absorption rate of the
stain without the additive is µ = 40 units. The engineer places the stain with the additive on n =
50 pieces of decking material and records? = 36.4 and s = 13.1.Determine the level of
significance for testing Ha: µ<40. Is there significant evidence in the data to support the
contention that the additive has decreased the mean absorption rate of the stain using an α
= 1%?

1. (Use rejection region approach)

Answer 1

Solution:
Given in the question
The claim is the data to support the contention that the additive has decreased the mean absorption rate of the stain so null and alternate hypothesis can be written as
Null hypothesis H0: µ = 40
Alternate hypothesis Ha: µ < 40
Number of sample(n) = 50
Sample mean (Xbar) = 36.4
Sample standard deviation(S) = 13.1
Here we will use t test as population standard deviation is not known so test stat value can be calculated as
Test stat = (Xbar - µ)/S/sqrt(n) = (36.4-40)/13.1/sqrt(50) = -1.943
This is left tailed test, and Degree of freedom = sample size - 1 = 50 - 1 = 49 and level of significance = 0.01
So test critical value from t table is -2.40
Decision Rule: If test stat value is less than -2.40 than reject the null hypothesis else do not reject the null hypothesis
Here we can see that test stat value is greater than -2.40. so we are failed to reject the null hypothesis. and we dont have significant evidence to support the claim that the data to support the contention that the additive has decreased the mean absorption rate of the stain.