In: Statistics and Probability
Heights of Mothers and Daughters. Listed below are heights (in.) of mothers and their first daughters. The data are from a journal kept by Francis Galton. (See Data Set 5 “Family Heights” in Appendix B.) Use a 0.05 significance level to test claim that there is no difference in heights between mothers and their first daughters.
Height of Mother 68.0 60.0 61.0 63.5 69.0 64.0 69.0 64.0 63.5 66.0
Height of Daughter 68.5 60.0 63.5 67.5 68.0 65.5 69.0 68.0 64.5 63.0
Since we have paired data of mother and daughter height so we will use paired t test as we do not have infomration about population standard deviation.
Here Difference in heigh =Mother height -daughter height
now we have to test that if mother height is different from the daughter height therefore we will test that if population average of difference of height is equal to ZERO or different from ZERO so
now from the data we have
sample size=n=10
sample mean of difference ==-0.95
sample standard deviation of difference =Sd=2.18
Now test statistics is given by
where t is t distribution with DF=n-1=10-1=9
since test is two-tailed and test statistics value is negative so P-value is given by(using t table)
P-Value =2*P(t<-1.38) =2*0.10=0.20
Since P-Value is higher than the level of significance (0.05) hence we failed to reject H0 hence there is no enough evidence to conclude that mother height is different from daughter height.