Mathematical Questions Confidence Interval Practice - 550 Words

Mathematical Questions: Confidence Interval Practice (Math Problem Sample) Content: NameTutorCourseDateConfidence Interval PracticeScenario: 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 student s 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 intervalSample 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) = 75.69Calculate the Lower Bound:M (t coefficient * SE)Lower bound = 73.16 - (1.96*1.29) = 70.63Lower 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_________Criti cal 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) = 76.46Calculate the Lower Bound:M (t coefficient * SE)Lower bound = 73.16 - (2.56*1.29) = 69.86Lower 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; lets 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...