Question

5. 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. (5)

PLEASE HELP!!

Answer 1

Solution :

Given that,

This a right (One) tailed test.

The null and alternative hypothesis is,  

Ho: 4.3

Ha: 4.3

The test statistics,

t =( - )/ (s /n)

= ( 5.4 - 4.3 ) / ( 5 / 56 )

= 1.646

Critical value of  the significance level is α = 0.05, and the critical value for a right-tailed test is

= 1.673

P- Value = 0.0527   

The p-value is p = 0.0527 > 0.05, it is concluded that the null hypothesis is fail to rejected.

There is not sufficient evidence that the mean pollutant level in a region is higher than the state average of 4.3 grams/cubic liter.