SOLUTION: In 2001, the mean household expenditure for energy was $1493, according to a survey. An economist wanted to know whether this amount has changed significantly from its 2001 level.

Question 1181350: In 2001, the mean household expenditure for energy was $1493, according to a survey. 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 mean expenditure (in 2001 dollars) for energy during the most recent year to be $1618, with a standard deviation $321. Is there evidence to conclude that the mean household expenditure for energy has increased since 2001? Use the α = 0.01 level of significance.
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Here's how to conduct a hypothesis test to answer this question:
**1. State the Hypotheses:**
* **Null Hypothesis (H₀):** The mean household expenditure for energy has not increased since 2001. (μ ≤ $1493)
* **Alternative Hypothesis (H₁):** The mean household expenditure for energy has increased since 2001. (μ > $1493) This is a right-tailed test.
**2. Determine the Level of Significance:**
α = 0.01
**3. Calculate the Test Statistic:**
Since the sample size is greater than 30, we can use a z-test. The formula for the z-statistic is:
z = (sample mean - population mean) / (standard deviation / sqrt(sample size))
z = (1618 - 1493) / (321 / sqrt(35))
z = 125 / (321 / 5.916)
z = 125 / 54.26
z ≈ 2.30
**4. Determine the Critical Value:**
For a right-tailed test with α = 0.01, we look up the z-score that corresponds to 0.99 in the standard normal distribution table (or use a calculator). The critical value is approximately 2.33.
**5. Make a Decision:**
Our calculated z-statistic (2.30) is *less than* the critical value (2.33). Therefore, we *fail to reject* the null hypothesis.
**6. State the Conclusion:**
There is *not* sufficient evidence at the 0.01 level of significance to conclude that the mean household expenditure for energy has increased since 2001. Although the sample mean is higher, the difference is not statistically significant.

RELATED QUESTIONS
1750 households in the UK were surveyed. The average weekly expenditure on food was found (answered by ewatrrr)

In city A, it is known that the mean monthly energy usage per household has historically... (answered by stanbon)

According to an estimate, the mean income of attorneys was $66,272 in 2011. A researcher... (answered by ewatrrr)

P&G wants to find out the mean spending on bath soaps by an family per month.P&G... (answered by ikleyn)

8.34 Working Women In an Advertising Age white paper concerning the changing role of... (answered by proyaop)

Last year income (in minimum wages) in city A was well represented by X ~ N (2,5; 4). An... (answered by Boreal)

1.A sample of 36 students are drawn from the NUST student population, and their body... (answered by greenestamps)

One of the variables collected in the North Carolina Birth Registry data (A-3) is pounds... (answered by ewatrrr)

the price of a coffee has increased by 25% . what percentage of coffee consumption is to... (answered by KMST)