Question

The China Health and Nutrition Survey aims to examine the effects of the health, nutrition, and family planning policies and programs implemented by national and local governments. It, for example, collects information on number of hours Chinese parents spend taking care of their children under age 6. The side- by-side box plots below show the distribution of this variable by educational attainment of the parent. Also provided below is the ANOVA output for comparing average hours across educational attainment categories. 

Answer 1

To test the hypothesis is that there is a difference between the average number of hours spent on child care across educational attainment levels at \(5 \%\) level of significance.

a)

The null and alternative hypothesisis,

$$ H_{0}: \mu_{1}=\mu_{2}=\mu_{3}=\mu_{4}=\mu_{5} $$

\(H_{a}:\) atleast one \(\mu_{i}\) is unequal.

b)

The \(F\)-test statistics is,

From the ANOVA output, the \(F\)-test statistics is \(1.26\).

The \(p\)-value for this test is,

From the ANOVA output, the \(p\) value for this test is \(0.2846\).

Decision

The conclusion is that \(p\)-value in this context is higher than \(0.05\) which is \(0.2846\), so the null hypothesis is not rejected at \(5 \%\) level of significance. There is insufficient evidence to indicate that there is a difference between the average number of hours spent on child care across educational attainment levels. The result is statistically significant.

The answer option is 3 .

Answer 2

From the given information,

The required correct answers are,

a. The correct hypotheses is,

Here, Third option is correct for hypotheses.

b.

Test statistic= 1.26

P-value= 0.2846

Thank you.