Answered: It is claimed that the average amount…

Name: 15. It is claimed that the average amount of time boys and girls (age
Uploaded: 2024-03-20T07:06:41.000Z
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Description: 15. It is claimed that the average amount of time boys and girls (age between 7 and 11) spend playing each day is the same. A child psychologist believes that boys, on average, spend more time playing sports than girls. He randomly selected 45 girls

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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15.

It is claimed that the average amount of time boys and girls (age between 7 and 11) spend playing each day is the same. A child psychologist believes that boys, on average, spend more time playing sports than girls. He randomly selected 45 girls and 95 boys and observed their play time on sports. From his samples he found that girls have spend on average 2.7 hours, and boys have spent on average 3.7 hours playing sports. It is found that the time spent playing sports is normally distributed for girls with a standard deviation of 0.31 hours and for boys with a standard deviation of 1.16 hours. Is this day sufficient to support the psychologist claim? Do the test at 5% level of significance. Assume girls belong to population 1 and boys belong to population 2. Data given in this question are:

	a)	y-bar1 = 2.7, y-bar2 = 3.7, s1 = 0.31, s2 = 1.16
	b)	mu1 = 2.7, mu2 = 3.7, s1 = 0.31, s2 = 1.16
	c)	mu1 = 2.7, mu2 = 3.7, sigma1 = 0.31, sigma2 = 1.16
	d)	y-bar1 = 2.7, y-bar2 = 3.7, sigma1 = 0.31, sigma2 = 1.16

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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