Answered: 39) Find 22 a. 44 b. 254 C. 628 d. 2309…

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

Researchers conducted a study to find out if there is a difference in the use of online-learning by different age groups. Randomly selected participants were divided into two age groups. In the 16 to 29-year-old group, 7% of the 628 surveyed use online-learning, while 11% of the 2,309 participants 30 years old and older use online learning. (Set 1 for 16-29 year old group; Set 2 for 30 years old and older). Find X2.

Expert Solution

Step 1

Given Information:

16 - 29 years old:

Sample size ( $n_{1}$ ) = 628

Sample proportion ( ${\hat{p}}_{1}$ ) = 7% = 0.07

30 years old & above:

Sample size ( $n_{2}$ ) = 2309

Sample proportion ( ${\hat{p}}_{2}$ ) = 11% = 0.11

To find the value of $X_{2}$ :

Sample proportion is given by the formula:

$\hat{p} = \frac{X}{n}$

where, $X$ is the number of successes and $n$ is the sample size.

We need to find the number of successes (number of individuals who use online learning) of set 2 i.e., 30 years and above:

Substitute the values of sample proportion and sample size and solve for X as follows:

$\begin{array}{rcl} {\hat{p}}_{2} & = & \frac{X_{2}}{n_{2}} \\ 0.11 & = & \frac{X_{2}}{2309} \\ X_{2} & = & 0.11 \times 2309 \\ X_{2} & = & 253.99 \\ \approx & 254 \end{array}$

Thus, the value of $X_{2}$ is 254

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