Answer to Question #115876 in Statistics and Probability for Shane Jessica Ballera

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.