Answered: For each situation, state the null and…

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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Question

For each situation, state the null and alternative hypotheses: (Type "mu" for the symbol μ , e.g. mu > 1 for the mean is greater than 1, mu < 1 for the mean is less than 1, mu not = 1 for the mean is not equal to 1. Please do not include units such as "mm" or "$" in your answer.)

Transcribed Image Text:### Understanding Hypothesis Testing through Examples #### Example (a): Spindle Diameter in a Small Motor The diameter of a spindle in a small motor should ideally be 4.9 millimeters (mm) with a standard deviation of 0.14 mm. Maintaining this precise measurement is crucial for the proper functioning of the motor. The manufacturer measures the diameter of a sample of 8 spindles to check if the average diameter has deviated from the specified size. Suppose the sample has an average diameter of 5.03 mm. - **Null Hypothesis (H₀):** The mean diameter is 4.9 mm. - **Alternative Hypothesis (Hₐ):** The mean diameter is not 4.9 mm. #### Example (b): Price Comparison of Laundry Detergent in Caldwell vs. Nationwide Harry suspects that prices in Caldwell are lower than the national average. According to his research, the nationwide average price of a specific brand of laundry detergent is $24.65, with a standard deviation of $1.94. Harry samples prices from 3 local Caldwell stores and finds the average price to be $25.44. - **Null Hypothesis (H₀):** The average price in Caldwell is equal to the nationwide average. - **Alternative Hypothesis (Hₐ):** The average price in Caldwell is lower than the nationwide average.

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 + ...

Expert Solution

Step 1: Concept of writing Null and Alternative hypothesis

Null Hypothesis (H1): It is known that a null hypothesis is a hypothesis which is under test or a type of statistical hypothesis that proposes no statistical significance.

Alternative Hypothesis (H0): An alternative hypothesis is simply the contradictory statement of a Null Hypothesis.