The cost of a college education has increased at a much faster rate than costs in general over the past twenty years.In order to compensate for this,many students work part- or full-time in addition to attending classes.At one university,it is believed that the average hours students work per week exceeds 20.To test this at a significance level of 0.05,a random sample of n = 20 students was selected and the following values were observed: Based on these sample data,the critical value expressed in hours:
A)is approximately equal to 25.26 hours.
B)is approximately equal to 25.0 hours.
C)cannot be determined without knowing the population standard deviation.
D)is approximately 22 hours.

Question

The cost of a college education has increased at a much faster rate than costs in general over the past twenty years.In order to compensate for this,many students work part- or full-time in addition to attending classes.At one university,it is believed that the average hours students work per week exceeds 20.To test this at a significance level of 0.05,a random sample of n = 20 students was selected and the following values were observed:  Based on these sample data,the critical value expressed in hours:
A)is approximately equal to 25.26 hours. 
B)is approximately equal to 25.0 hours. 
C)cannot be determined without knowing the population standard deviation. 
D)is approximately 22 hours.

Quizplus · Accepted Answer

Since the sample size is small (n=20) and the population standard deviation is unknown, we need to use a t-distribution with n-1 degrees of freedom to determine the critical value. For a 95% confidence level and 19 degrees of freedom, the critical value is approximately 2.093. Therefore, the critical value expressed in hours is equal to 20 + (2.093)(2) = 25.186, which can be rounded to 25.26 hours.

The Cost of a College Education Has Increased at a Much