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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

Expert verified

\(\chi^{2}\) test statistics \(=16.489268\)

And \(p-value=0.0573412\)

\(p-value>\alpha\)

Therefore the decision will be fail to reject the null hypothesis,\(H_{0}\) . Therefore, the null hypothesis does not get rejected and is accepted. Hence, it can be concluded that there are sufficient evidence to ensure that the actual literacy rates are same.

Step by step solution

01

Step 1. Given information

Student in social studies class hypothesize that the literacy rates across the world for every region are \(82%\0. The below given table shows the actual literacy rates across the world broken down by region:

MDG Region

Adult Literacy Rate (%)

Developed Regions

99.0

Commonwealth of Independent States

99.5

Northern Africa

67.3

Sub-Saharan Africa

62.5

Latin America and the Caribbean

91.0

Eastern Asia

93.8

Southern Asia

61.9

South-Eastern Asia

91.9

Western Asia

84.5

Oceania

66.4

02

Step 2. Calculation

The null hypothesis can be stated as:

\(H_{0}:\) Actual literacy rates are same.

And the alternative hypothesis can be stated as:

\(H_{a}:\) Actual literacy rates are different.

Now, let’s do the calculation in the excel as shown below;

The p-value can be calculated in excel by using formula as shown below:

\(\chi^{2}\) test statistics \(=16.489268\)

And \(p-value=0.0573412\)

We have the alpha value given as \(0.05\). Now, since \(p-value>\alpha\) therefore the decision will be fail to reject the null hypothesis, \(H_{0}\). Therefore, the null hypothesis does not get rejected and is accepted. Hence, it can be concluded that there are sufficient evidence to ensure that the actual literacy rates are same.

The null hypothesis can be stated as:

\(H_{0}:\) Actual literacy rates are same.

And the alternative hypothesis can be stated as:

\(H_{a}:\) Actual literacy rates are different.

Therefore the decision will be fail to reject the null hypothesis, \(H_{0}\). Therefore, the null hypothesis does not get rejected and is accepted. Hence, it can be concluded that there are sufficient evidence to ensure that the actual literacy rates are same.

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