Question

You survey 284 students about whether they use a laptop or tablet. One hundred

Answer 1

In a two-way frequency table, the marginal frequencies is the 'total' entry for the row and the 'total' entry for the column

The result of the data organized in a two way table with the marginal frequency included is as follows;

$\begin{array}{|l|c|c|c|}\mathbf{\underline{Device \ Student \ Use}}&\mathbf{\underline{Laptop}}&\mathbf{\underline{Do\ not \ use \ laptop}}&\mathbf{\underline{Total}}\\&&&\\\mathbf{Tablet}&49 &75&\underline{124}\\&&&\\\mathbf{Do\ not \ use \ tablet}&63&97&\underline{160}\\&&&\\\mathbf{Total}&\underline{112}&\underline{172}&284\\&&&\end{array}$

The reason the above table is correct is as follows:

The known parameters are;

Number of students in the survey, U = 284 students

The number of students that use a laptop, n(L) = 112

The number of students that also use a tablet, T ∩ L = 49

The number of students that do not use a laptop or a tablet, $n(T \cup L)^c$  = 97

Required:

To organize the result of the survey in a two-way table

Solution:

U = $n(T \cup L)^c$ + n(T ∪ L)

Therefore;

n(T ∪ L) = U - $n(T \cup L)^c$

n(T ∪ L) = 284 - 97 = 187

n(T ∪ L) = 187

The number of students that use only a laptop = n(L) - n(T ∩  L) = 112 - 49 = 63

The number of students that use only a laptop [n(L) - n(T ∩  L)] = 63

n(T ∪ L) = n(T) + n(L) - n(T ∩ L)

n(T) = n(T ∪ L) - [n(L) - n(T ∩ L)]

n(T) = 187 - 63 = 124

The number of students that use only tablets = n(T) - n(T ∩  L) = 124 - 49 = 75

The number of students that use only tablets, [n(T) - n(T ∩  L)] = 75

 

The results are organized in the attached two way table and the marginal frequencies are the numbers underlined in the totals column

$\begin{array}{|l|c|c|c|}\mathbf{\underline{Device \ Student \ Use}}&\mathbf{\underline{Laptop}}&\mathbf{\underline{Do\ not \ use \ laptop}}&\mathbf{\underline{Total}}\\&&&\\\mathbf{Tablet}&49 &75&\underline{124}\\&&&\\\mathbf{Do\ not \ use \ tablet}&63&97&\underline{160}\\&&&\\\mathbf{Total}&\underline{112}&\underline{172}&284\\&&&\end{array}$

Learn more about marginal frequencies here:

brainly.com/question/16401512