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# 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

#### 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.

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