Question

According to the document Consumer Expenditures, a publication of the Bureau of Labor Statistics, the average consumer unit spent $1736 on apparel and services in 2012. That same year, 25 consumer units in the Northeast had the following annual expenditures, in dollars, on apparel and services.

1279   1457   2020   1682   1273

2223   2233   2192   1611   1734

2688   2029   2166   1860   2444

1844   1765   2267   1522   2012

1990    1751 2113   2202   1712

At the 5% significance level, do the data provide enough evidence to conclude that the 2012 mean annual expenditure on apparel and services for consumer units in the Northeast differed from the national mean of $1736?

1. Define the null and the alternative hypotheses.

2. Using the classical approach to provide the p-value and the test statistic t0.

3. Using the p-value approach to provide the p-value and the test statistic t0.
4. Using t.test in R provide the p-value and the test statistic t0.
5. Can you reject or cannot reject the null hypothesis, justify your answer based on both the classical and the p-value approaches?

Answer 1

The hypothesis being tested is:

H₀: µ = 1736

H_a: µ ≠ 1736

The output is:

1,736.000	hypothesized value
1,922.760	mean Data
350.899	std. dev.
70.180	std. error
25	n
24	df
2.06	critical t
2.661	t
.0137	p-value (two-tailed)

The test statistic is 2.661.

The critical value is 2.06.

The p-value is 0.0137.

Classical approach:

Since 2.661 > 2.06, we can reject the null hypothesis.

Therefore, we have insufficient evidence to conclude that the 2012 mean annual expenditure on apparel and services for consumer units in the Northeast differed from the national mean of $1736.

P-value approach:

Since the p-value (0.0137) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we have insufficient evidence to conclude that the 2012 mean annual expenditure on apparel and services for consumer units in the Northeast differed from the national mean of $1736.