Question

The mean drying time of a brand of spray paint is known to be 90 seconds. The research division of the company contemplates that adding a new I'm a coal ingredient to the paint will accelerate the drying process. The mean and standard deviation for a sample of 15 is 86 seconds and 4.5 seconds, respectively using the new additive. Should they add the new chemical ingredient?

Answer 1

Step 1:

Ho: = 90

Ha: < 90

Step 2: Test statistics

n = 15

sample mean = 86

sample sd = 4.5

Assuming that the data is normally distributed and also as the population sd is not given, we will calculate t stat

t = - 3.443

Step 3:

As the level of significance is not given, we take = 0.05

df = 14

t critical for left tailed test = - 1.761

As the t stat is falls in the rejection area, we reject the Null hypothesis.

hence we have sufficient evidence to believe that the mean drying time is less than 90 sec.

So, they should  add the new chemical ingredient