c) In order to investigate the effect of gender on the birth weight of the baby, birth weight information of 56 babies was obtained by sampling according to the classification among the birth information cards of babies born in 2016.

Question

baby boys baby girls
Sample mean (Ẋ) 3.250 kg 3.400 kg
Sample standard deviation (S) 0.400 0.500
Number of observations (n) 28 28

Since it is known that it fits the normal distribution in both distributions, is there any difference between these two groups in terms of gender? First write the hypothesis and test it at the error level of α= 0.05 and interpret the results.

Answer 1

Hypothesis:
H0: There is no difference between the birth weights of baby boys and baby girls.
Ha: There is a difference between the birth weights of baby boys and baby girls.

Test statistic:
t = (Ẋ1 - Ẋ2) / (S1^2/n1 + S2^2/n2)^0.5

t = (3.250 - 3.400) / (0.400^2/28 + 0.500^2/28)^0.5

t = -0.735

At the error level of α= 0.05, the critical value of t is 1.671. Since the calculated t value is lower than the critical value, we fail to reject the null hypothesis. This means that there is no statistically significant difference between the birth weights of baby boys and baby girls.

Answer 2

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