Question
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Compute in excel A college admission officer for an MBA program determines that historically candidates have...
Compute in excel
A college admission officer for an MBA program determines that historically candidates have undergraduate grade averages that are normally distributed with standard deviation of .45. A random sample of 25 applications from the current year yields a sample mean grade point average of 2.90. (i) Find a 95% confidence interval for the population mean, μ. (Round the boundaries to 2 decimal places.) (ii) Based on the same sample results, a statistician computes a confidence interval for the population mean as 2.81< μ < 2.99. Find the α for this interval and the probability content (1- α) as well. (Round to 4 digits.) (Note: the correct α is a higher number than traditional α used; so don’t worry if your number “looks” wrong!) Hint: first calculate α/2 using either the lower bound (2.81) or upper bound (2.99); then calculate α. Finally, calculate the probability content of the interval, which is (1- α). And make sure you use the standard error, not the standard deviation, to calculate α/2.
Solutions
Expert Solution
Solution:
We are given:
(i) Find a 95% confidence interval for the population mean, μ.
Answer: The 95% confidence interval for the population mean is:
Therefore, the 95% confidence interval for the population mean is (2.72, 3.08)
(ii) Based on the same sample results, a statistician computes a confidence interval for the population mean as 2.81< μ < 2.99.
We know that:
Now we have to find the area corresponding to z = 1.
Using the standard normal table, we have:
Now the area to the right of 0.8413 is 
Therefore, the significance level used is 
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