Medical researchers have noted that adolescent females are much more likely to d
ID: 3159151 • Letter: M
Question
Medical researchers have noted that adolescent females are much more likely to deliver low-birth-weight babies than are adult females. Because low-birth-weight babies have a higher mortality rate, a number of studies have examined the relationship between birth weight and mother’s age. One such study is described in the article “Body Size and Intelligence in 6-Year-Olds: Are Offspring of Teenage Mothers at Risk?” (Maternal and Child Health Journal {2009]: 847-856). The following data on maternal age (in years) and birth weight of baby (in grams) are consistent with summary values given in the article.
age<-c(15, 17, 18, 15, 16, 19, 17, 16, 18, 19)
weight<-c(2289, 3393, 3271, 2648, 2897, 3327, 2970, 2535, 3138, 3573)
a) find the correlation coefficient value and interpret the value
b) find the coefficient of determination and interpret this value
c) at the 5% level of significance, test to see if there is a correlation. Show all steps of the hypothesis test.
Explanation / Answer
a) Find the correlation coefficient value and interpret the value
Solution:
The correlation coefficient value is given as 0.883694 which means there is a high or strong positive linear relationship or linear association exists between the two variables age and weight.
b) Find the coefficient of determination and interpret this value
Solution:
The coefficient of determination or the value for R square is given as 0.883694* 0.883694 = 0.780915 which means about 78.09% of the variation in the dependent variable weight is explained by the independent variable age.
c) At the 5% level of significance, test to see if there is a correlation. Show all steps of the hypothesis test.
Solution:
Here, we have to test whether there is a correlation exists or not. We have to use the t test for correlation coefficient.
The null and alternative hypothesis for this test is given as below:
Null hypothesis: H0: There is no correlation exists between age and weight.
Alternative hypothesis: Ha: There is a correlation exists between age and weight.
We are given level of significance or alpha value = 5% or 0.05
The test statistic formula is given as below:
Test statistic = t = r / sqrt[(1 – r^2)/(n – 2)]
Here, we are given r = 0.8837 and n = 10
Test statistic = t = 0.8837 / sqrt [(1 – 0.8837^2)/(10 – 2)]
Test statistic = t = 5.340158
P-value is less than 0.05
So, we reject the null hypothesis that there is no correlation exists between age and weight.
This means we conclude that there is a correlation exists between age and weight.