Answered: Independent random samples of 17…

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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Question

Independent random samples of 17 sophomores and 13 juniors attending a large university yield the following data on grade point averages:

sophomores juniors

x bar 2.84 2.75

n 17 13

s 0.52 0.31

Add the 5% significance level, does the data provide sufficient evidence to conclude that the mean GPAs of sophomores at the University are better than the juniors?

1. choose the correct parameter for the problem

a. Mu₁_: the average GPAs of all sophomores attending a large university ; Mu₂_: the average GPAs of all juniors attending a large university

b. All sophomores attending a large university; all juniors attending a large university

c. The average GPA of all students attending a large university

d. xbar_{1: the average GPAs of all sophomores attending a large university;}xbar₂: the average GPA's of all juniors attending a large University

2. Select the correct hypotheses for the problem

a. HO: mu₁= Mu₂, HA mu₁< mu₂

b.HO: mu_{1 <} Mu₂, HA mu_{1 >} mu₂

c. HO: mu₁= Mu₂, HA mu₁not equal to mu₂

d. HO: mu₁= Mu₂, HA mu_{1 >} mu₂

3. calculate the appropriate values (use four decimal places) show all your work on a separate sheet of paper

S_p= ? t=?

Select the correct decision and conclusion for the problem:

a. Do not reject HO, we have sufficient evidence to conclude that the mean GPAs of sophomores at the University are better than the juniors

b. Reject HO, we have sufficient evidence to conclude that the mean GPAs of sophomores at the university or better than the juniors

c. Reject HO, we do not have sufficient evidence to conclude that the mean GPAs of sophomores at the university are better than the junior

d. Do not reject HO, we do not have sufficient evidence to conclude that the mean GPAs of sophomores at the University are better than the juniors

Thank you!!!

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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