Answered: Let x represent the average annual…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Topic Video

Question

Let x represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of x is approximately σ² = 47.1. However, a random sample of 16 colleges and universities in Kansas showed that x has a sample variance s² = 85.2. Use a 5% level of significance to test the claim that the variance for colleges and universities in Kansas is greater than 47.1.

(a) State the null and alternate hypotheses.

H₀: σ² < 47.1; H₁: σ² = 47.1

H₀: σ² = 47.1; H₁: σ² ≠ 47.1

H₀: σ² = 47.1; H₁: σ² > 47.1

H₀: σ² = 47.1; H₁: σ² < 47.1

(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)

(c) What assumptions are you making about the original distribution?

We assume a uniform population distribution.

We assume a exponential population distribution.

We assume a binomial population distribution.

We assume a normal population distribution.

(d) Find or estimate the P-value of the sample test statistic.

P-value > 0.100

0.050 < P-value < 0.100

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

P-value < 0.005

(e) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Since the P-value > α, we fail to reject the null hypothesis.

Since the P-value > α, we reject the null hypothesis.

Since the P-value ≤ α, we reject the null hypothesis.

Since the P-value ≤ α, we fail to reject the null hypothesis.

(f) Interpret your conclusion in the context of the application.

At the 5% level of significance, there is insufficient evidence to conclude the variance of annual salaries is greater in Kansas.

At the 5% level of significance, there is sufficient evidence to conclude the variance of annual salaries is greater in Kansas.

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

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Hypothesis Tests and Confidence Intervals for Means$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions