Answered: A random sample of 47 observations was…

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 random sample of 47 observations was selected from a normally distributed population. The sample mean was x = 97.7, and the sample variance was s² = 35.1. Does this sample show sufficient reason to conclude that the population standard deviation is not equal to 7.2 at the 0.05 significance level?

(a) State the appropriate null and alternative hypotheses.
H_o: σ ? < > = ≠ 7.2
H_a: σ ? < > = ≠ 7.2

(ii) Find χ². (Give your answer correct to two decimal places.)

(iii) Find the p-value. (Give your answer bounds exactly.)
< p <

(b) State the appropriate conclusion.

Reject the null hypothesis, there is not significant evidence that the population standard deviation differs from 7.2.Reject the null hypothesis, there is significant evidence that the population standard deviation differs from 7.2. Fail to reject the null hypothesis, there is not significant evidence that the population standard deviation differs from 7.2.Fail to reject the null hypothesis, there is significant evidence that the population standard deviation differs from 7.2.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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