Answered: Use the StatCrunch output provided to…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 26PFA

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Use the StatCrunch output provided to answer the following (parts a-g. The output was obtained by using a person’s foot length (cm) to predict their height (cm) for a sample of 40 people.

a. What is the correlation between foot length and height?

b. Estimate the change in the mean height when the foot length increases by one cm. Use a 95% confidence interval.

c. Conduct a hypothesis test to determine if there is a linear association between X and Y. Use α = .05.

d. Obtain and interpret a 95% confidence interval for the mean height for a people with a foot length of 25.5 cm..

e. Obtain a 95% prediction interval for a person that has a foot length of 26.2.

f. One person had a foot length of 25.4 cm and a height of 165.7 cm. Find the residual for this observation.

g. Give and interpret (in context) the coefficient of determination for this problem.

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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