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Critical value, confidence level

Please see the attached file.

1. What is the appropriate critical value for each of the following confidence levels and sample sizes? (Remember that in regard to confidence level this implies two-tails)

(a) Critical z-value for an 85% confidence level for sample of size n = 36:

(b) Critical t-value for a 90% confidence level for sample of size n = 20:

2 How do you know when to use a t-distribution and associated critical t-values as opposed to a z-distribution and critical z-values within a confidence interval or hypothesis testing situation?

3. A graduate student is interested in determining the average GPA of all FHSU undergraduate students, but the student does not have access to all records. A random sample of 35 FHSU undergraduate students provided the data which appears to the right.

(a) Determine the mean and standard deviation of this sample data.

(b) Determine the expected margin of error amount in using this sample result to estimate the average GPA of all FHSU undergraduate students based upon a 95% desired level of confidence.

(c) Determine the 90% confidence interval for the mean GPA of all FHSU undergraduate students.

(d) State your final confidence interval result in a sentence that interprets the result within the context of the situation.

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