A research organization has been investigating the effect of family size on cons

Question

A research organization has been investigating the effect of family size on consumer spending habits. In a random sample of 200 families of three members each, they found that an average of 0.38 (38%) income was spent on housing. In another sample of 100 families of six members each, average of 0.31 (31%) of family income was spent on housing. In both cases, the sample variance of the proportion spent on housing was 0.06. Is the percentage of income spent for housing significantly different for families of three versus families of six? If so, would you conclude that family size caused the difference in spending habits? Explain. Could regression analysis have been used effectively to investigate the relation between housing expenditure, family income, and family size? If so, what data would you have the research organization collect? What models/regressions would you run and what tests or procedures would you use to help you interpret the results?

Explanation / Answer

Null Hypothesis : Spent on housing are not different for different family size

Alternate Hypothesis : Spending varies with family size

n1 = 200 , Sample size for 3 member family

n2 = 100 , Sample size for 6 member family

Lets first do it by simple t test for mean difference

Now to simplify our hypothesis

Null Hypothesis : Difference of their means is zero

Alternate : Non zero mean difference

t - statistic = [(0.38-0.31) - 0]/ d

d = Standard error of mean difference = Sq.root[(S1^2/n1) + (S2^2/n2)]

S = Std dev and n is the sample size

S1^2 = S2^2 = 0.06

For regression modelling in R

We can perform linear regression using following syntax

data <- read.csv(“file path”, sep=“”)

fit <- lm(Y~X , data = data)

summary(fit)

Summary gives us the p value attached to each coefficients attached to all the parameters ( like family income, family size) which helps us to determine the significance of each parameter in contributing to our model. High p value means low significance.

If we will gonna compare more than two models then we can ANOVA to compare which model is more significant.

Syntax : anova(model1, model2)

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