Question

Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 7.5 parts/million (ppm). A researcher believes that the current ozone level is not at a normal level. The mean of 16 samples is 7.8 ppm with a standard deviation of 0.8. Assume the population is normally distributed. A level of significance of 0.01 will be used. Make the decision to reject or fail to reject the null hypothesis.

Answer 1

We accept H₀ with the information we have, we can say level of ozone is under the major limit

Explanation:

Normal Distribution

population mean = μ₀ = 7.5 ppm

Sample size n = 16 df = n - 1 df = 15

Sample mean = μ = 7.8 ppm

Sample standard deviation = s = 0.8

We want to find out if ozono level, is above normal level that is bigger than 7.5

1.- Hypothesis Test

null hypothesis H₀ μ₀ = 7.5

alternative hypothesis Hₐ μ₀ > 7.5

2.-Significance level α = 0.01 we will develop one tail-test (right)

then for df = 15 and α = 0,01 from t -student table we get

t(c) = 2.624

3.-Compute t(s)

t(s) = ( μ - μ₀ ) / s /√n ⇒ t(s) = ( 7.8 - 7.5 )*4/0.8

t(s) = 0.3*4/0.8

t(s) = 1.5

4.-Compare t(s) and t(c)

t(s) < t(c) 1.5 < 2.64

Then t(s) is inside the acceptance region. We accept H₀