Question

Consider a paint-drying situation in which drying time for a test specimen is normally distributed with s = 6. The hypotheses H0: µ = 74 and Ha: µ < 74 are to be tested using a random sample of n = 25 observations.(a) How many standard deviations (of X) below the null value is x = 72.3? (Round your answer to two decimal places.)(b) If x = 72.3, what is the conclusion using a = 0.01? (Round your answers to two decimal places.)test statistic z =critical value z =What can you conclude?

Answer 1

There is no statistical evidence to support the claim that the mean is elss than 74.

Explanation:

Given that a paint-drying situation in which drying time for a test specimen is normally distributed with s = 6.

The hypotheses H0: µ = 74 and Ha: µ < 74

are to be tested using a random sample of n = 25 observations

a) Z =
`(72.3-74)/((6)/(√(25) ) ) \\=-1.417`

ie. -1.417 std deviations to the left of mean.

b) p value = 0.078241

Since p > 0.01 , our alpha, accept H0

There is no statistical evidence to support the claim that the mean is elss than 74.