At Western University the historical mean of scholarship examination scores for

Question

At Western University the historical mean of scholarship examination scores for freshman applications is 900. A historical population standard deviation = 165 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.

a. State the hypotheses.
H0: Selectgreater than or equal to 900greater than 900less than or equal to 900less than 900equal to 900not equal to 900Item 1
Ha: Selectgreater than or equal to 900greater than 900less than or equal to 900less than 900equal to 900not equal to 900Item 2

b. What is the 95% confidence interval estimate of the population mean examination score if a sample of 200 applications provided a sample mean = 935 (to the nearest whole number)?
( , )

c. Use the confidence interval to conduct a hypothesis test. Using = .05, can the assistant dean conclude that the mean examination score for the new freshman applications has changed?
SelectYesNoItem 5

d. What is the p-value (to 3 decimals)?

Explanation / Answer

(a) Ho: = 900 versus Ha: 900

(b)

n = 200     

x-bar = 935     

s = 165     

% = 95     

Standard Error, SE = /n =    165 /200 = 11.66726189

z- score = 1.959963985     

Width of the confidence interval = z * SE =     1.95996398454005 * 11.667261889578 = 22.8674131

Lower Limit of the confidence interval = x-bar - width =      935 - 22.8674131017697 = 912.1325869

Upper Limit of the confidence interval = x-bar + width =      935 + 22.8674131017697 = 957.8674131

The 95% confidence interval is [912.13, 957.87]

(c) Since 900 is outside the above interval, there is sufficient evidence that the mean has changed.

(d) p- value = 0.003

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