Monthly food expenditures for families in rodriguez rizal averaged php6,500 with

n=7xˉ=n∑x​=736​=5.14285714s2=n−1∑x2−n(∑(x))2​​=6220−185.142857​=5.8095s=s2​=5.8095​=2.4103

The hypotheses are,

$H_0:\mu=4.25\\vs\\H_1:\mu\gt4.25$

The test statistic is,

$t={\bar x-\mu\over {s\over\sqrt{n}}}={5.14-4.25\over{2.4103\over\sqrt{7}}}={0.8929\over0.911}=0.98$

The critical value is,

$t_{\alpha,n-1}=t_{0.1,6}=1.439756$

The null hypothesis is rejected if, $t\gt t_{0.1,6}$

Since $t=0.98\lt t_{0.1,6}=1.439756$, the null hypothesis is not rejected. Therefore, we can conclude that there is no sufficient evidence to show that the average family size is more than the national average at 1% level of significance.