Question

In 2001, the mean household expenditure for energy was $1493, according to data obtained from the U.S. Energy Information Administration. An economist wanted to know whether this amount has changed significantly from its 2001 level. In a random sample of 35 households, he found the sample mean to be $1618 and the sample standard deviation to be $321. Test the claim that the mean expenditure has changed siginificanlty from the 2001 level at the 0.05 level of significance. State your conclusion

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u= 1493
Alternative hypothesis: u 1493

Note that these hypotheses constitute a two-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 54.2589

DF = n - 1

D.F = 34
t = (x - u) / SE

t = 2.304

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the t statistic having 34 degrees of freedom is less than -2.304 or greater than 2.304.

Thus, the P-value = 0.027

Interpret results. Since the P-value (0.027) is less than the significance level (0.05), we have to reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that mean expenditure has changed siginificanlty from the 2001.