Question

# The chancellor at City University is worried that the grades have fallen in the past year....

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

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.

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