A company is researching the effectiveness of a new website design to decrease the time to access a website. Five website users were randomly selected,and their times (in seconds)to access the website with the old and new designs were recorded. To compare the times,they computed new website design time − old website design time. The results follow. For a 0.01 significance level,what is the critical value?
A)−2.256
B)−1.895
C)−3.747
D)−2.447

Question

A company is researching the effectiveness of a new website design to decrease the time to access a website. Five website users were randomly selected,and their times (in seconds)to access the website with the old and new designs were recorded. To compare the times,they computed new website design time − old website design time. The results follow.  For a 0.01 significance level,what is the critical value?
A)−2.256 
B)−1.895 
C)−3.747 
D)−2.447

Quizplus · Accepted Answer

To find the critical value, we need to use a t-distribution with n-1 degrees of freedom, where n is the sample size (n=5). Since we have a 0.01 significance level and a two-tailed test, we need to find the t-value that corresponds to a 0.005 area in both tails of the distribution. Using a t-distribution table, we find that the critical value with 4 degrees of freedom (n-1) is -3.747. Therefore, the answer is choice C.

A Company Is Researching the Effectiveness of a New Website