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

Given:

= 4.3, n = 56, = 5.4, SD(S) = 5.0

Hypothesis:

Ho: = 4.3

Ha: > 4.3

Test statistic:

Degree of freedom = n-1 = 56-1 = 55

Critical value:

                 ...................Using t table

P-value = 0.0527                 ...................Using t table

Conclusion:

t < t, n-1, that is 1.65 < 1.6730, That is Fail to Reject Ho at 5% level of significance

OR

P-value > α, i.e. 0.0527 > 0.05, That is Fail to Reject Ho at 5% level of significance.

Therefore, there is Not sufficient evidence to conclude that the, researcher suspects that the mean pollutant level in a region is higher than the state average of 4.3 grams/cubic liter