# The Mean Examination Score

The historical mean of scholarship examination scores for freshman applications at a local university is 900. A historical population standard deviation of 180 is assumed known. Each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed. Use a 95% confidence interval. A sample of 200 applications provided a sample mean of 935.
Has the mean examination score for new freshman changed?

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...or the new freshman applications has changed. Use a 95% confidence interval. A sample of 200 applications provided a sample mean of 935.
Has the mean examination score for new freshman changed?
Solution:
Here n = 200, Mean = 935, Standard Deviation =180
 = 5%, so Z/2 = 1.96
Confidence interval =  Z/2 ×
= 935  1.96 ×
=935 ...