Question

The chancellor at City University is worried that the grades have fallen in the past year. The grade point average for graduating students in the previous 5 years was 2.80 with a standard deviation of 0.25. The chancellor randomly samples 10 seniors from this year's graduating class and obtains the following GPAs: 2.40, 2.80, 2.65, 2.15, 2.65, 2.72, 2.42, 2.70, 2.52, 2.49. What can the chancellor conclude? Use a two-tailed test at the.05 significance level

Answer 1

H0: Null Hypothesis: = 2.80

HA: Alternative Hypothesis: 2.80

From the given data, the following statistics are calculated:

n = 10

= 2.55

s = 0.1937

SE = s/

= 0.1937/

= 0..0613

Test statistic is given by:

t = (2.55 - 2.80)/0.0613

= - 4.0783

= 0.05

ndf = n - 1 = 10 - 1 = 9

From Table, critical values of t = 2.2622

Since the calculated value of t = - 4.0783 is less than critical value of t = - 2.2622, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the Chancellor's worry that the grades have fallen in th past year.