Q.R11.2 - The Practice of Statistics for AP

Question

Sorry, no chi-square We would prefer to learn from teachers who know their subject. Perhaps even pre-school children are affected by how knowledgeable they think teachers are. Assign $48$ three- and four-year-olds at random to be taught the name of a new toy by either an adult who claims to know about the toy or an adult who claims not to know about it. Then ask the children to pick out a picture of the new toy in a set of pictures of other toys and say its name. The response variable is the count of right answers in four tries. Here are the data:

The researchers report that children taught by the teacher who claimed to be knowledgeable did significantly better $\left({\chi }^2=20.24,P<0.05\right)$. Explain why this result isn't valid.

Step-by-Step Solution

Answer

There are $6$ cells which have expected count less than $5$.

Step 1: Given Information

The observed number of counts in four tries is as follows

${\chi }^2=20.24$

$P<0.05$.

Step 2: Explanation

Concept used:

For chi square test to be used, in each cell the expected count should be more than or equal to $5$.

Formula used:

Expected count $=\frac{\text{ row total }\times \text{ column total }}{\text{ total of all rown or columns }}$

Calculation:

The expected count will be

Using the concept aforementioned, there are $6$ cells which have expected count less than $5$.

Hence, the result isn't valid because chi square can't be used.