# Test of hypothesis using t distribution

(a) At alpha (a) =.05, does the following sample show that daughters are taller than their mothers?

(b) Is the decision close?

(c) Why might daughters tend to be taller than their mothers? Why might they not?

Family Daughters Height(CM) Mothers Height (CM)

1 167 172

2 166 162

3 176 157

4 171 159

5 165 157

6 181 177

7 173 174

https://brainmass.com/statistics/students-t-test/test-of-hypothesis-using-t-distribution-222336

#### Solution Preview

(a) At alpha (a) =.05, does the following sample show that daughters are taller than their mothers?

(b) Is the decision close?

(c) Why might daughters tend to be taller than their mothers? Why might they not?

Family Daughters Height(CM) Mothers Height (CM)

1 167 172

2 166 162

3 176 157

4 171 159

5 165 157

6 181 177

7 173 174

(a) At alpha (a) =.5, does the following sample show that daughters are taller than their mothers?

First calculate the mean and standard deviation of the two sample.

Daughters Height(CM)

X= X 2 =

167 27889

166 27556

176 30976

171 29241

165 27225

181 32761

173 29929

Total= 1199 205577

n=no of observations= 7

Mean= 171.29 =1199/7

variance={summation of X 2 - n(Mean) 2 }/(n-1)= 32.5252 =(205577-7*171.29^2)/(7-1)

standard deviation =square root of Variance= 5.7031 =square root of 32.5252

Mothers' Height(CM)

X= X 2 =

172 29584

162 26244

157 24649

159 25281

157 24649

177 31329

174 30276

Total= 1158 192012

n=no ...

#### Solution Summary

Tests the hypothesis that the daughters are taller than their mothers.