Hypothesis Test of the


Example: A sample of 10 families revealed
the following figures for family size and the amount spent on food per
week.

Size  3  6  5  6  6  3  4  4  5  3 
$  99  104  151  129  142  111  74  91  119  91 
Solution: “Can we ... a positive association ... food and
the family size"
means the same as “the coefficient of correlation is greater than zero.” Therefore, the null and alternate
hypotheses are H_{0}: r £
0 and H_{1}: r > 0, respectively. Follow the steps
below to solve the problem using the TI83.
[NOTE: If the pvalue < a, reject the null hypothesis; otherwise, do not
reject the null hypothesis.]
Press STAT, EDIT, 1:Edit, and enter the data in L1 (independent variable) and L2 (dependent variable). 

Press
STAT, TESTS, and press the down arrow to E:LinRegTTest. 

Select the alternate hypothesis > 0. Note the line RegEQ:Y1. This will help produce the graph later. Use the down arrow to get to calculate and press ENTER. 

Results: Since the pvalue is 0.0365 < 0.05, reject the null hypothesis. Conclude that there is a positive relationship between the amount spent on food and family size. The coefficient of correlation is 0.5892, and the coefficient of determination is 0.3471. Thus, about 34.7% of the variation in food expense is accounted for by variation in family size. 

To graph the scattered diagram with the linear regression line, press ZOOM 9. 
