Question

Hypothesis Testing

Some people claim that the amount of rainfall this month is very much the same as the great rains of 2010 whose average volume is 450mm with a standard deviation of 100mm. when you checked this month‟s data; you found that the average rainfall from five storms was 180mm. Are the people‟s lay theories correct at α 0.05? Use traditional and p-value method.

Answer 1

$H_0:\mu=450$

$H_1:\mu\not=450$

This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

Based on the information provided, the significance level is $\alpha=0.05,$ and the critical value for a two-tailed test is $z_c=1.96.$

The rejection region for this two-tailed test is $R=\{z:|z|>1.96\}$

The z-statistic is computed as follows:

$$Z={\bar{X}-\mu\over \sigma/\sqrt{n}}={180-450\over 100/\sqrt{5}}=-6.037$$

Using the P-value approach: The p-value is $p=0,$ and since $p=0<0.05,$ it is concluded that the null hypothesis is rejected. Therefore, there is enough evidence to claim that the population mean $\mu$

is different than 450, at the 0.05 significance level.