Question

A random sample of $900$students at a very large university was asked which social-networking site they used most often during a typical week. Their responses are shown in the table below.

Assuming that gender and preferred networking site are independent, which of the following is the expected count for female and LinkedIn?

$a)18.85$$b)46.11$$c)87.00$$d)91.65$$e)103.35$

Short answer

The answer is option$e)103.35$

Step-by-step solution

Given Information

We have been given the total number of students at a very large university is$900$.

We need to find the expected count for females and LinkedIn.

Simplification

When the two factors for a two-way table are independent, the expected value formula is just the number of samples times the two probabilities.

$P\left(F\right)=\frac{c_2}{n}$, $P\left(L\right)=\frac{r_3}{n}$

$mean=n\times P\left(F\right)\times P\left(L\right)$

localid="1650524309687" $mean=\frac{c_2\times r_3}{n}$

where c₂ is column 2 total, r₃ is row 3 total, and n is the grand total. This is taken from the table.

Therefore, $c_2=477$, $r_3=195$, $n=900$.

$mean=\frac{477\times 195}{900}$.

On calculating, we get:

$mean=103.35$