Answered: 1.In a trial for the university…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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1.In a trial for the university athletics competition, one aims to estimate the mean chest size of the male athletes. A random sample of 70 male athletes gave rise to an average chest size of 42 inches with a standard deviation of 16 inches. What would be the distribution of the statistic that we need to estimate the mean chest size?

a. it is normal distribution with mean 42 and standard deviation 16 inches.

b. it is a student's t distribution with degree freedom 69

c. it is a student's t distribution with mean 42 inches and standard deviation 16 inches.

d. It is a normal distribution with degree of freedom 69.

2.What would be the margin of error for a 95% confidence interval of the true chest size in problem 1?

a. 0.46

b. 0.52

c. 3.82

d. 4.38

3.How do you conclude using the 95% confidence interval?

a. With 95% confidence, the sample mean chest size is between 38.18 inches and 45.82 inches.

b. With 95% confidence, the sample mean chest size is between 37.62 and 46.38.

c. With 95% confidence, the true mean chest size is between 37.62 inches and 46.38 inches.

d. With 95% confidence, the true mean chest size is between 38.18 inches and 45.82 inches.

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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