Answered: Confidence Interval A simple…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Confidence Interval

A simple random sample of 56 students who picked up all tests they completed was selected, and the mean score on final exam for this sample of students was 83 with a standard deviation of 10.4. An independent simple random sample of 51 students who had one or more tests that were not picked up was selected, and the mean score on the final exam for this sample of students was 67 with a standard deviation of 24.2. Both distributions are skewed heavily to the left [note: this is the same information provided in question above]. If appropriate, use this information to calculate and interpret a 99% confidence interval for the difference in the mean score on the final exam for all students who picked up all their tests and the mean score on the final exam for all students who had one or more tests that were not picked up.

In question above a 99% confidence interval was computed. If the confidence level were decreased to 90%, what impact would this have on the margin of error and width of the confidence interval?

a) Both the margin of error and the width would decrease.

b) Neither the margin of error nor the width would be affected.

c) The margin of error would increase and the width would decrease

d) The margin of error would decrease and the width would increase.

e) Both the margin of error and the width would increase.

Based on the decision, which of the following is the correct conclusion?

a) There is insufficient evidence that the mean final exam grade for all students who picked up all their tests is the same as the mean final exam grade for all students who had one or more tests that were not picked up.

b) There is insufficient evidence that the mean final exam grade for all students who picked up all their tests is greater than the mean final exam grade for all students who had one or more tests that were not picked up.

c) There is sufficient evidence that the mean final exam grade for all students who picked up all their tests is the same as the mean final exam grade for all students who had one or more tests that were not picked up.

d) There is sufficient evidence that the mean final exam grade for all students who picked up all their tests is greater than the mean final exam grade for all students who had one or more tests that were not picked up.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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