Answered: Student High School GPA Attended a…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter12: Angle Relationships And Transformations

Section12.1: Angle Relationships

Problem 44E

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Question

You have the following random sample containing information on undergraduate students at liberal arts colleges. The population standard deviation is unknown. The sample standard deviation is equal to 0.4272. Round to 2 decimal places.

A) Estimate the mean High School GPA for undergraduate students at liberal arts colleges.
B) Calculate the upper and lower bound of a 95% confidence interval for mean G.P.A.
C) Calculate the upper and lower bound of a 90% confidence interval for mean G.P.A.

Student
High School GPA
Attended a Private High School
1
3.3
No
2345
2.9
No
3.0
No
3.1
Yes
2.7
Yes
6
2.6
No
7
4.0
No
8
3.8
Yes
9
2.8
Yes
10
3.6
Yes
11
3.1
No
12
3.0
No
13
2.7
No
14
2.9
Yes
15
3.4
Yes
16
3.7
No

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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