QuestionSuppose a geologist believes that the average chloride concentration in her local water supply is above the national average of 156 ppm . The geologist defines a null hypothesis, $H_{0}: \mu=156 \mathrm{ppm}$, to reflect the mean chloride concentration in the national water supply. She formulates an alternative hypothesis, $H_{1}: \mu>156 \mathrm{ppm}$, to indicate that her locality has a higher concentration of chloride in its water supply, on average. In these hypotheses, $\mu$ represents the true mean concentration of chloride in the local water supply. The geologist samples groundwater from across her locality and determines that the average concentration of chloride in her sample is 208 ppm , with a standard deviation of 35 ppm . Experience has shown that these data can be treated as random samples from a normal population. The geologist uses a one-sample, right-tailed $t$-test for a mean to test her hypotheses. She computes a $t$-statistic with a value of 7.862 and 27 degrees of freedom.
Decide the outcome of the geologist's test using a significance level of $\alpha=0.05$. Fail to reject the null hypothesis because the $P$-value is greater than $\alpha$. Reject the null hypothesis because the $P$-value is greater than $\alpha$.