Question

Students in a social studies class hypothesize that the literacy rates across the world for every region are $82\%$. Table $11.14$shows the actual literacy rates across the world broken down by region. What are the test statistic and the degrees of freedom?

Short answer

The alpha value has been set at $0.05$. Because $p-value>\alpha$, the decision to reject the null hypothesis,$H_0$ , will be failed. As a result, the null hypothesis is accepted rather than rejected. As a result, there is sufficient evidence to conclude that the real literacy rates are the same.

Step-by-step solution

Given information

Given in the question that, Students in a social studies class hypothesize that the literacy rates across the world for every region are$82\%$. Table $11.14$shows the actual literacy rates across the world broken down by region.

We need to find the test statistic and the degrees of freedom.

Explanation

The null hypothesis is written as follows:

$H_0:$The actual literacy rates are identical.

The alternate hypothesis is as follows:

$H_a:$The actual literacy rates varies.

Let's now perform the calculation in Excel, as shown below:

The p-value can be determined using the $CHIDIST\left(\right)$formula in Excel, as illustrated below:

${\chi }^2$test statistic $=16.489268$

$\&$P-value$=0.0573412$

The alpha value has been set at $0.05$. Because $p-value>\alpha$, the decision to reject the null hypothesis, $H_0$., will be failed. As a result, the null hypothesis is accepted rather than rejected. As a result, there is sufficient evidence to conclude that the real literacy rates are the same.