Answer:
Yes. The male and female consumers differ in the amounts they spend.
Step-by-step explanation:
We can express the null and alternative hypothesis as:
[tex]H_0: \mu_m=\mu_w\\\\H_1: \mu_m\neq\mu_w[/tex]
It is assumed a significance level of 0.05.
The standard deviation of the difference of means is calculated as:
[tex]s=\sqrt{\frac{s_m^2}{n_m} +\frac{s_w^2}{n_w} } =\sqrt{\frac{35^2}{40} +\frac{20^2}{30} } =\sqrt{30.625+13.333} =\sqrt{43.958} =6.63[/tex]
The test statistic is
[tex]t=\frac{(M_m-M_w)-0}{s}=\frac{135.67-68.64}{6.63}=10.11[/tex]
The degrees of freedom are:
[tex]df=n_1+n_2-2=40+30-2=68[/tex]
The P-value for t=10.11 is P=0, so it is smaller than the significance level. The null hypothesis is rejected.
We can conclude that male and female consumers differ in the amounts they spend.
