Answered: Test the claim that the mean GPA of…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section: Chapter Questions

Problem 8SGR

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Test the claim that the mean GPA of night students is smaller than 3.3 at the .025 significance level.

The null and alternative hypothesis would be:

H0:μ=3.3 H1:μ≠3.3

H0:p=0.825 H1:p≠0.825

H0:μ=3.3 H1:μ<3.3

H0:p=0.825 H1:p<0.825

H0:μ=3.3 H1:μ>3.3

H0:p=0.825 H1:p>0.825

The test is:

two-tailed

right-tailed

left-tailed

Based on a sample of 80 people, the sample mean GPA was 3.28 with a standard deviation of 0.08

The test statistic is: (to 2 decimals)

The critical value is: (to 2 decimals)

Based on this we:

Fail to reject the null hypothesis
Reject the null hypothesis

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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