Question

(8.3.11) Park officials make predictions of times to the next eruption of a particular​ geyser, and collect data for the errors​ (minutes) in those predictions. The display from technology available below results from using the prediction errors to test the claim that the mean prediction error is equal to zero. Comment on the accuracy of the predictions. Use a 0.05 significance level. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.
Assuming all conditions for conducting a hypothesis test are​ met, what are the null and alternative​ hypotheses?

Answer 1

For this case they want to test this:

H0: 

H1: 

So the correct option is:

B. Upper H0​: μ=0 minutes

Upper H1​: μ≠0 minutes

The significance level its $\alpha=0.05$

The statistic on this case is calculated with the following formula:

$t= \frac{x-\mu}{\frac{s}{\sqrt{n}}}$

t(observed value) =-7.44

Using Z table , for 0.05 significance t(Critical value )= 1.984

DF = 98

From z table ,p value (two tailed) < 0.0001

We reject the null hypothesis because the $p < \alpha$ . So we can conclude that the difference is significantly different from 0 at 5% of significance.