Answered: Floretta, a gym owner, claims that her…

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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Reject H0. At the 1% significance level, the test results are not statistically significant and at best, provide weak evidence against the null hypothesis.

Reject H0. At the 1% significance level, the data provide sufficient evidence to conclude that the mean yearly new customers is more than 163 people.

Do not reject H0. At the 1% significance level, the test results are not statistically significant and at best, provide weak evidence against the null hypothesis.

Do not reject H0. At the 1% significance level, the data provide sufficient evidence to conclude that the mean yearly new customers is more than 163 people.

Floretta, a gym owner, claims that her yearly new customers are more than 163 people, on average. Several of her friends
do not believe her, so she decides to do a hypothesis test, at a 1% significance level, to persuade them. She collects data
from 25 previous years and works through the testing procedure:
167
·α = 0.01 (significance level)
The test statistic is
167 163
- 1.82
The critical value is z0.o1
2.33.
Conclude whether to reject or not reject Ho, and interpret the results.

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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