Answered: Hypothesis test of one mean. 1. An…

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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Hypothesis test of one mean.

1. An engineer wants to measure the bias in a pH Meter. She uses the meter to measure the pH in 12 neutral substances (pH = 7.0) and obtains the data shown below.

7.01, 7.04, 6.97, 7, 6.99, 6.97, 7.04, 7.04, 7.01, 7.00, 6.99, 7.07

Use the = 0.05 level of significance to test if the pH meter is calibrated correctly,

Hypothesis test of one proportion.

2. In 2012, 58% of females aged 15 years of age and older lived alone according the US Census Bureau. A sociologist want to know if the percentage is different today. She obtains a rander sample of 500 females aged 15 years or older and finds that 285 are living alone. Is there

evidence to suggest that there is a change at a = 0.01 level of significance.

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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