Answered: Research Question: Is there 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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Research Question: Is there a difference between the average height of male and female basketball players in the club?

28 male and 25 female basketball players from the club were randomly selected. Use the following image to answer the questions below.

Carry out an appropriate hypothesis test to answer the above Research Question.

Q1) The null and alternative hypotheses are : Choose one from below

-H₀: μ = 0, H₁: μ ≠ 0

-H₀: μ = 170, H₁: μ ≠ 170

-H₀: μ_m- μ_f= 167.489, H₁: μ_m- μ_f≠ 167.489

-H₀: μ_m- μ_f= 0, H₁: μ_m- μ_f≠ 0

H₀: μ_m- μ_f= 170.27, H₁: μ_m- μ_f≠ 170.27

Q2) What is the assumption you need to make ? Choose one from below

-The shape of the histogram indicates that the scores may be from a normal distribution and/or the sample size is reasonably large so the sample mean will be from a normal population

-None of these

-Since nπnπ and n(1−π)n(1−π) are both ≥5, the Central Limit Theorem applies and we can assume that p arises from a normal distribution

-The boxplots indicate that the samples are fairly symmetric and the spreads are similar, so we can assume both sets of data come from normal distributions with the same spread

-The points are randomly scattered around a straight line, so the assumptions of linearity and constant spread are satisfied. The shape of the histogram indicates that the residuals come from a normal distribution

Q3) What is the value of the test statistic? (3 decimal places)

Two Sample t-test
data: male_height and female_height
t = 3.763, df = 51, p-value
0.0004347
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
1.298592 4.268813
sample estimates:
mean of male_height mean of female_height
170.2727
167.4890

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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