Question

A researcher suspects that the mean pollutant level in a region is higher than the state average of 4.3 grams/cubic liter.  Data are collected; from 56 samples, the mean is found to be 5.4, with a standard deviation of 5.0.  Test the null hypothesis that the true mean in the region is 4.3, against the alternative that it is higher.  State the null and alternative hypotheses, give the critical value, find the test statistic, make a decision, and give the p-value.

Answer 1

Solution :

= 4.3

= 5.4

= 5.0

n = 56

This is the right tailed test .

The null and alternative hypothesis is ,

H0 :    = 4.3

Ha : > 4.3

Test statistic = z

= ( - ) / / n

= (5.4-4.3) / 5.0 / 56  

= 1.65

Test statistic = z = 1.65

P(z >1.65 ) = 1 - P(z < 1.65 ) = 1 - 0.9505

P-value =0.0495