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 26 samples is 7.1 ppm with a standard deviation of 1.0 . Assume the population is normally distributed. A level of significance of 0.02 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.

Answer 1

Solution :

Given that ,

= 7.5

= 7.1

= 1.0

n = 26

The null and alternative hypothesis is ,

H₀ :   = 7.5

H_a : > 7.5

This is the right tailed test .

Test statistic = z

= ( - ) / / n

= ( 7.1 - 7.5) / 1.0 / 26

= -2.04

The test statistic = -2.04

P - value = P(Z > -2.04 ) = 1- P (Z < -2.04 )

= 1 - 0.0207

= 0.9793

The P-value = 0.9793