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.

Answer 1

Considering the below given Data, let's calculate the values

Difference = 0.508
t (Observed value) = 7.16
| t | (Critical value) = 1.984
degree of freedom (dof) = 99   
p-value (Two- tailed) < 0.0001
significance level (alpha) = 0.05

Solution:

Null and Alternative Hypotheses:

Ho: Mean prediction Error = 0

Ha: Mean prediction Error 0

Test statistic = -7.16

P - value = 0.0000

Since, p - value is less than alpha so we reject Ho,

Therefore, we can say that there is sufficient evidence to prove the claim that the mean prediction error is equal to 0