Question

The drying time of a type of paint under specified test condition is known to be normally distributed with an assumed mean value of 75 and a standard deviation of 9. Test the hypothesis H0: µ=75 vs. Ha: µ<75 from a sample of 25 observations with a sample mean value of 72.3.  What is the p-value for this test (to 4 decimals)?

Answer 1

Given :

Sample size = n = 25

Sample mean = = 72.3

T

Standard deviation = $\sigma$ = 9

Hypothesis test :

The null and alternative hypothesis is

H0: µ=75 vs. Ha: µ<75

Test statistic :

z = ( ${\bar{x}}-\mu$ )/$\sigma$/√n

= (72.3 - 75)/9/√25

= -1.5

Test statistic is z = -1.5

p-value :

p-value = P(Z < -1.5) = 0.0668

Therefore the p-value for the test is 0.0668