Question

In 2001, the mean household expenditure for energy was $1493, according to data from the U.S. Energy Information Administration. An economist wants to test whether this amount has changed significantly from its 2001 level. In a random sample of 35 households, he found the mean expenditure for energy during the most recent year to be $1618, with a standard deviation $321. Conduct a hypothesis test at 10% significance level to see whether we have strong evidence to support the economist’s hypothesis.

Answer 1

Since the population variance is not known, we will conduct a t-test for testing the significance of ean household expenditure.

(It is assumed that the sample standard deviation so provided has not been corrected with Bessel's correction formula, such that E(standard deviation^2)= E(sample variance) Population variance. Therefore, I have made the correction myself.)

As we can see the t cal > t tabulated, therefore, we will reject the null hypothesis as the sample provides enough evidence to do so.

Therefore, it is to be concluded that there exists a significant difference between the 2001 amount and the current year amount of household expnediture.