Answered: Test the claim that the mean GPA of…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

Problem 8CR

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Question

Test the claim that the mean GPA of night students is larger than 2.2 at the 0.01 significance level.

The null and alternative hypothesis would be:

H0:p≤0.55H0:p≤0.55
H1:p>0.55H1:p>0.55

H0:p=0.55H0:p=0.55
H1:p≠0.55H1:p≠0.55

H0:μ≤2.2H0:μ≤2.2
H1:μ>2.2H1:μ>2.2

H0:μ≥2.2H0:μ≥2.2
H1:μ<2.2H1:μ<2.2

H0:μ=2.2H0:μ=2.2
H1:μ≠2.2H1:μ≠2.2

H0:p≥0.55H0:p≥0.55
H1:p<0.55H1:p<0.55

The test is:

left-tailed

right-tailed

two-tailed

Based on a sample of 75 people, the sample mean GPA was 2.22 with a standard deviation of 0.07

The test statistic is: (to 2 decimals)

The p-value is: (to 2 decimals)

Based on this we:

Reject the null hypothesis
Fail to 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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