The time to complete the Advanced Placement (AP) Statistics Exam in previous years is normally distributed with an average time of 2.5 hours. Because of school closures due to COVID-19, the College Board offered an at-home test for the 2020 AP Statistics Exam. A teacher feels that students, on average, will have a different completion time for the at-home exam. They take a random sample of 27 students that took the exam and their mean time was 2.69 hours with a standard deviation of 0.4 hours. Test to see if the mean time has significantly changed using a 5% level of significance. Give answers to at least 4 decimal places.

What are the correct hypotheses? 

H₀: Select an answer p̂ x̄ σ² μ σ s² s p ? = ≠ < ≤ > ≥ hours

H₁: Select an answer p μ σ² s² s σ p̂ x̄ ? ≥ = ≠ > ≤ < hours

Based on the hypotheses, find the following:

Test Statistic t =  

Critical-Value t = $\displaystyle \pm$ 

Shade the sampling distribution curve with the correct critical value(s) and shade the critical regions. The arrows can only be dragged to t-scores that are accurate to 1 place after the decimal point (these values correspond to the tick marks on the horizontal axis). Select from the drop down menu to shade to the left, to the right, between or left and right of the t-score(s), then drag shaded area to match your critical value(s).

The correct decision is to Select an answer Accept the null hypothesis Accept the alternative hypotheis Fail to reject the null hypothesis Reject the null hypothesis .

The correct summary would be: Select an answer There is enough evidence to reject the claim There is not enough evidence to reject the claim There is not enough evidence to support the claim There is enough evidence to support the claim that the population mean time to complete the SAT has significantly changed from 2.5 hours.