Mathematical Questions: Confidence Interval Practice (Math Problem Sample)

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Confidence Interval Practice
Scenario: In 2011, the John Jay Math department created a new curriculum for STAT 250. Instead of having to do mandatory assignments, students would have discretion as to the how many HW assignments they would do. The professor would upload 15 assignments and students completed only 8 assignments. At the end of the year, the Math department wanted to see how students that took STAT 250 in 2011 performed. They collected a random sample of 95 students and order to estimate their average final grade.
Section 1: Download the data set that is at the top of Topic 5, and calculate the following for the 95 students who are the sample for this study.
MEAN for sample ___= ∑x /n = 6950/95 = 73.16_____
Standard Deviation for sample _________12.58______
(Estimated) Standard Error of the Mean _____1.29__________
Sample Size (n)__95________
Section 2: The sample mean is the POINT ESTIMATE of the population mean (the average for all students if they all were taught with this method). But, the INTERVAL ESTIMATE (also called the Confidence Interval) will be more accurate. Calculate a 95% confidence interval
Sample Mean _______73.16______
Confidence Interval (CI)___X__<73.16<_X_____
Alpha _______0.05______
Critical T Value ____1.96_________
Standard Error for the sample__1.29___________
Calculate the Upper Bound:M + (t coefficient * SE)
Upper bound = 73.16 + (1.96*1.29) = 75.69
Calculate the Lower Bound:M – (t coefficient * SE)
Lower bound = 73.16 - (1.96*1.29) = 70.63
Lower bound of the INTERVAL ESTIMATE _________70.63__________
Upper bound of the INTERVAL ESTIMATE __________75.69___________
Section 3: Using the sample statistics above, calculate the 99% Confidence Interval. Notice any differences between this CI and the previous one?
Sample Mean ______73.16_______
Confidence Interval (CI)____X< 73.16 < X_________
Alpha ____0.01_________
Critical T Value _____2.56________
Standard Error for the sample____1.29_________
Calculate the Upper Bound:M + (t coefficient * SE)
Upper bound = 73.16 + (2.56*1.29) = 76.46
Calculate the Lower Bound:M – (t coefficient * SE)
Lower bound = 73.16 - (2.56*1.29) = 69.86
Lower bound of the INTERVAL ESTIMATE __________69.86__________
Upper bound of the INTERVAL ESTIMATE _________76.46____________
Section 4: Calculate a 95% confidence interval BUT this time stead of having 95 students in your sample; let’s assume that we have 500 students. HINT: the sample mean and standard deviation of the sample stays the same, but you will have to calculate a standard error for the sample m...