Answer:
To test whether household income has an impact on child height after accounting for mothers' height and rainfall at birth, you can set up a multiple regression analysis. Here's how you can fill in the blanks for your hypothesis and analysis:
Hypothesis:
Null Hypothesis (H0): Household income has no significant impact on child height after controlling for mothers' height and rainfall at birth.
Alternative Hypothesis (H1): Household income has a significant impact on child height after controlling for mothers' height and rainfall at birth.
Significance Level: Since you specified using a 5% significance level, you will set α (alpha) to 0.05. This means you are willing to accept a 5% chance of making a Type I error (rejecting the null hypothesis when it's true).
Analysis Steps:
Data Collection: Collect data on household income, child height, mothers' height, and rainfall at birth for your sample.
Multiple Regression Model: Use a multiple regression model to analyze the data. The model equation could look like this:
Child Height = β0 + β1(Mothers' Height) + β2(Rainfall at Birth) + β3(Household Income) + ε
β0, β1, β2, and β3 are coefficients to be estimated.
ε represents the error term.
Hypothesis Testing: Use the regression analysis to test the null hypothesis. You will specifically want to test whether the coefficient for Household Income (β3) is statistically significant.
If the p-value associated with the coefficient for Household Income (β3) is less than 0.05, you would reject the null hypothesis and conclude that household income has a significant impact on child height after controlling for the other variables.
If the p-value is greater than 0.05, you would fail to reject the null hypothesis, indicating that household income does not have a significant impact on child height after accounting for mothers' height and rainfall at birth.
Interpretation: If you reject the null hypothesis, you can interpret the coefficient for Household Income to understand the direction and strength of its impact on child height while controlling for the other variables.
Remember that the results should be interpreted cautiously, and correlation does not imply causation. Other factors that are not included in the model could also influence child height, so the analysis should be part of a broader investigation.
Step-by-step explanation: