Question

A doctor wants to research if there is any difference in the birth weights of a mother's first child and second child. Suppose that data were collected for a random sample of 10 mothers with 2 children, where each difference is calculated by subtracting the weight of the first child from the weight of the second child. Assume that the weights are normally distributed. The doctor uses the alternative hypothesis Ha:μd≠0. Suppose the test statistic t is calculated as −1.101, which has 9 degrees of freedom. If the p-value is greater than 0.10 and the significance level is α=0.10, what conclusion can be made about the birth weights of a mother's first 2 children?

Answer 1

There is not sufficient evidence to conclude that there exists significant difference in the birth weights of a mother's first child and second child at 10% level of significance.

Explanation:

When our p-value exceeds level of significance then we fail to reject our null hypothesis. In this scenario we are investigating if there exists significant difference in the birth weights of a mother's first child and second child and our null hypothesis is there exists no significant difference in the birth weights of a mother's first child and second child i.e.μd=0.

As we are given that p-value is greater than 10% level of significant so, we cannot reject our null hypothesis. Thus, the conclusion statement can be written as "There is not sufficient evidence to conclude that there exists significant difference in the birth weights of a mother's first child and second child at 10% level of significance."