A student is interested in knowing if there is a relationship between theage of a child and the amount of time spent on the computer. He asks 7people their ages and the number of hours they spend on the computer.Is there a relationship between age and the amount of time spent oncomputers? Test at a = .05 level of significance.Age of child (yrs)Time on computer (hrs)11174.104.1138.

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Description: A student is interested in knowing if there is a relationship between theage of a child and the amount of time spent on the computer. He asks 7people their ages and the number of hours they spend on the computer.Is there a relationship between age a

Given: S.No x y 1 11 5 2 17 7 3 4 0 4 7 2 5 10 4 6 5 1 7 13 8 1.Null Hypothesis…

Answered: A student is interested in knowing if…

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 student is interested in knowing if there is a relationship between the
age of a child and the amount of time spent on the computer. He asks 7
people their ages and the number of hours they spend on the computer.
Is there a relationship between age and the amount of time spent on
computers? Test at a = .05 level of significance.
Age of child (yrs)
Time on computer (hrs)
11
17
4.
10
4.
1
13
8.

Expert Solution

Step 1

Given:

S.No	x	y
1	11	5
2	17	7
3	4	0
4	7	2
5	10	4
6	5	1
7	13	8

1.Null Hypothesis H₀: There is no relationship between age and amount of time spent on computer.

$H_{0} : ρ = 0$

2.Alternative Hypothesis H₁: There is a relationship between age and amount of time spent on computer.

$H_{1} : ρ \neq 0$

Step 2

3.Level of Significance : Level of Significance is given as $α = 0.05$ .

4. Test Statistic :

$t = \frac{r \sqrt{n - 2}}{\sqrt{1 - r^{2}}}$

Where correlation r can be calculated from the formula,

$\begin{array}{rcl} r & = & \frac{n \sum_{}^{} x y - \sum_{} x \sum_{} y}{\sqrt{(n \sum_{} x^{2} - {(\sum_{} x)}^{2}) (n \sum_{} y^{2} - {(\sum_{} y)}^{2})}} \end{array}$

Correlation 'r' is calculated as below:

S.No	x	y	$x y$	$x^{2}$	$y^{2}$
1	11	5	55	121	25
2	17	7	119	289	49
3	4	0	0	16	0
4	7	2	14	49	4
5	10	4	40	100	16
6	5	1	5	25	1
7	13	8	104	169	64
Total	67	27	337	769	159

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