Question

Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 6.1 parts/million (ppm). A researcher believes that the current ozone level is not at a normal level. The mean of 81 samples is 6.0 ppm with a standard deviation of 0.6. Assume the population is normally distributed. A level of significance of 0.05 will be used. State the null and alternative hypotheses.

Answer 1

Solution :

This is the two tailed test,  

The null and alternative hypothesis is ,

H0 :   = 6.1

Ha :    6.1

Test statistic = t =

= ( - ) / s / n

= (6.0 - 6.1) / 0.6 / 81

Test statistic = t = -1.50

degrees of freedom = n - 1 = 81 - 1 = 80

P(t < -1.50) = 0.0688

P-value = 2 * P(t < -1.50)

P-value = 2 * 0.0688

P-value = 0.1376

= 0.05  

P-value >

Fail to reject the null hypothesis .