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Description: A physical fitness trainer has several workouts she developed for increasing female upper body strength. All the workout plans are created based on the average adult women’s bench press ability. The average adult woman can bench 115 lbs. with a stan

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A physical fitness trainer has several workouts she developed for increasing female upper body strength. All the workout plans are created based on the average adult women’s bench press ability. The average adult woman can bench 115 lbs. with a standard deviation of 18 pounds. The trainer has a class of 14 females and does an initial test to see if the women are representative of the average female population.

Write the null and alternative hypothesis in statistical form:

Determine the mean for the sample:

Apply the z-test formula:

Is this a one-tailed (directional test) or a two-tailed (non-directional test)?

What is your alpha level set to? α =

Determine the critical value(s) (Z_crit) =

Label the critical value(s) and indicate the position of the Z_obt on the distribution

Write the z result in the correct form:

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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Given

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$F o r t h e a v e r a g e a d u l t w o m a n p o p u l a t i o n, m e a n b e n c h p r e s s w e i g h t : μ = 115 l b s w i t h s \tan d a r d d e v i a t i o n : σ = 18 p o u n d s$

The trainer has a class of 14 females and does an initial test to see if the women are representative of the average female population.

Hence,

$s a m p l e s i z e : n = 14$

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