Question

A teacher predict that the distribution of grades on the final exam will be and they are recorded in table 11.27

The actual distribution for a class of 20 is in table 11.28

$X^2$test statistic is -------

Short answer

$X^2$test statistic is$2.04$

Step-by-step solution

Given Information 

Given tables are

we have to determine$X^2$test statistics.

Explanation  

We know that there are$1000$total frequencies. As a result, we multiply each frequency by $1000$and calculate the table below.

The following steps will be used to calculate the ${\chi }^2$test statistic.

1. In the first column of the excel sheet, we write the expected frequencies.

2. Fill in the first column of the excel sheet with the observed frequencies.

3. Create a column titled (Observed - Expected)

4. Create a new column to calculate the square of the result (Observed Expected)

5. Divide the square of (Observed - Predicted) by the expected frequencies of each observation in the last column.

6. Finally, we add the last two columns together.

Let's now perform the calculation in Excel as follows:

$X^2$test statistic is$\approx 2.04$