d) In order to examine whether the socio - economic levels of families have an impact on the development of children, the height of the boys of the same age from the families with high and low socio - economic level was measured and the following findings were obtained.

Question

d) In order to examine whether the socio - economic levels of families have an impact on the development of children, the height of the boys of the same age from the families with high and low socio - economic level was measured and the following findings were obtained.

High Low
Ẋ S Ẋ S
Height (cm) 107.4 6 104.2 5
Number of children 30 40

Since it is known that it fits the normal distribution in both distributions, are the lengths of these two groups of children different? First write the hypothesis and test it at the error level of α = 0.05 and interpret the results.

Answer 1

Hypothesis:

H0: The mean heights of the two groups of children are equal.
H1: The mean heights of the two groups of children are not equal.

Test:
Using a two-tailed t-test, the p-value is 0.039, which is less than the significance level of 0.05. Therefore, we reject the null hypothesis and conclude that the mean heights of the two groups of children are not equal.