Question

Are moms shorter than their daughters? This is the question we want to look into. The following data set shows gives the height of 20 randomly selected moms and the corresponding heights of their daughters . Use a 1% significance level to test the claim that mothers are shorter than their daughters. Be sure to give the null and alternative hypothesis, the test statistics the p-value, whether you reject the null hypothesis and a conclusion.

Mom's Height: 62.7,60.5,64.2, 62.1, 60.3.60.4, 60.8,67.2,59.3,61.8, 62.2, 66, 65.7, 65.7, 63.7, 65.1, 63.6, 64.9, 63.8, 62.9

Daughter's Height: 63.1, 60.2, 65.8, 63.7, 60, 61.4, 62, 65.3, 60.1, 63.7, 63.9,67.1, 65, 67.2, 64.5, 65.8, 61.4, 65.2, 63.5, 62

Answer 1

using minitab

enter the data in minitab and use the two independent sample t test we have the following output

N Mean StDev SE Mean
Mom Height 20 63.15 2.22 0.50
daughter height 20 63.55 2.24 0.50

Difference = μ (Mom Height) - μ (daughter height)
Estimate for difference: -0.400
99% upper bound for difference: 1.313
T-Test of difference = 0 (vs <): T-Value = -0.57 P-Value = 0.287 DF = 37
since p value is greater than 0.01 so we accept the null hypothesis , we do not have sufficient evidence to accept the claim