At a certain American university, the average attendance at basketball games has been 2,700 spectators per game. The attendance for the first 16 games has been 2,450 spectators per game with a standard
Deviation of 550. The athletic director claims that the attendance is the same as last year. If , what
Are the critical values?
A) $\pm 1.7531$
B) $\pm 2.1315$
C) $\pm 3.5062$
D) $\pm 4.2630$

Question

At a certain American university, the average attendance at basketball games has been 2,700 spectators per game. The attendance for the first 16 games has been 2,450 spectators per game with a standard
Deviation of 550. The athletic director claims that the attendance is the same as last year. If  , what
Are the critical values? 
A) $\pm 1.7531$ 
B) $\pm 2.1315$ 
C) $\pm 3.5062$ 
D) $\pm 4.2630$

Quizplus · Accepted Answer

We need to use a t-test since the sample size is less than 30 and the population standard deviation is unknown. The null hypothesis is that the attendance is the same as last year, which means the population mean is equal to 2,700. The alternative hypothesis is that the attendance is different from last year, which means the population mean is not equal to 2,700. Since the question does not mention the significance level, we can assume it to be 0.05 (two-tailed). With 15 degrees of freedom (n-1), the critical value for rejecting the null hypothesis is $\pm 2.1315$ (from t-table or calculator). Therefore, we can reject the null hypothesis if the calculated t-value is greater than 2.1315 or smaller than -2.1315.

At a Certain American University, the Average Attendance at Basketball ±1.7531\pm 1.7531±1.7531

At a Certain American University, the Average Attendance at Basketball $\pm 1.7531$