Answered: A random sample of size 29 from a…

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

A random sample of size 29 from a normal distribution has variance s² = 24. Test H₀ : σ² ≥ 30 versus H₁ : σ² < 30.

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.

Expert Solution

Step 1

A random sample of size 29 from a normal distribution has variance s²=24.

The test hypotheses are given below:

Null hypothesis: H0: σ² ≥ 30

Alternative hypothesis: H1: σ² < 30

Test statistic:

Software Procedure:

Step-by-step procedure to obtain the test statistic using the MINITAB software:

Choose Stat > Basic Statistics > 1 Variance.
Under Data, choose Sample variance.
Enter Sample size as 29.
Enter Sample variance as 24.
Check Perform hypothesis test.
Choose Hypothesized variance, enter the Value as 30.
Check Options, enter Confidence level as 0.95.
Choose less than in alternative.
Click OK.

Output using the MINITAB software is given below:

From the output, the test statistic is 22.4 and the P-value is 0.238.

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