Question

The average expenditure on Valentine's Day was expected to be $100.89 (USA Today, February 13, 2006). Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 40 male consumers was $135.67, and the average expenditure in a sample survey of 30 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $35, and the standard deviation for female consumers is assumed to be $20. The z value is 2.576 .

Answer 1

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:

$H_0: \mu_m=\mu_w\\\\H_1: \mu_m\neq\mu_w$

It is assumed a significance level of 0.05.

The standard deviation of the difference of means is calculated as:

$s=\sqrt{\frac{s_m^2}{n_m} +\frac{s_w^2}{n_w} } =\sqrt{\frac{35^2}{40} +\frac{20^2}{30} } =\sqrt{30.625+13.333} =\sqrt{43.958} =6.63$

The test statistic is

$t=\frac{(M_m-M_w)-0}{s}=\frac{135.67-68.64}{6.63}=10.11$

The degrees of freedom are:

$df=n_1+n_2-2=40+30-2=68$

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.