Question

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. Difference: -0.479 t​ (Observed value): -7.60 ​ | t​ | (Critical​ value): 1.986 DF: 94 ​ p-value (Two-tailed): <0.0001 alpha: 0.05

Answer 1

Identify the null and alternative​ hypotheses

H0 : i.e. the mean prediction error is equal to zero

H1 : i.e. the mean prediction error is not equal to zero

Test​ statistic (as provided)

t​ (Observed value): -7.60

P-value (as provided)

p-value (Two-tailed): <0.0001

State the final conclusion

Since p-value < 0.05, we reject H0. There is strong evidence against the null hypothesis. We conclude that the the mean prediction error is not equal to zero.