Final answer:
To test the claim that the mean waste recycled by adults in the country is more than 1 pound per person per day, we need to set up the null and alternative hypotheses and calculate the test statistic. Comparing the test statistic to the critical value, we can determine if the claim is supported at the given significance level. In this case, we reject the null hypothesis and have enough evidence to support the claim.
Step-by-step explanation:
Question:
An environmentalist estimates that the mean waste recycled by adults in the country is more than 1 pound per person per day. You want to test this claim. You find that the mean waste recycled per person per day for a random sample of 15 adults in the country is 1.4 pounds and the standard deviation is 0.4 pound. At α = 0.10, can you support the claim? Assume the population is normally distributed. Write the claim mathematically and identify H₀ and Ha. Find the critical value(s) and identify the rejection region(s).
Answer:
To test the claim, we need to set up the null hypothesis H₀ and the alternative hypothesis Hₐ. In this case, the null hypothesis is that the mean waste recycled is equal to or less than 1 pound per person per day (H₀: µ ≤ 1), and the alternative hypothesis is that the mean waste recycled is greater than 1 pound per person per day (Hₐ: µ > 1).
To determine if the claim can be supported, we calculate the test statistic using the data provided. The test statistic is calculated as (sample mean - population mean) / (standard deviation / √sample size). Plugging in the values, we get (1.4 - 1) / (0.4 / √15) ≈ 3.354. We then compare this test statistic to the critical value(s) from the t-distribution table. With α = 0.10 and df = 14 (degrees of freedom, calculated as sample size - 1), the critical value is approximately 1.761.
Since the test statistic (3.354) is greater than the critical value (1.761), we reject the null hypothesis. This means that we have enough evidence to support the claim that the mean waste recycled by adults in the country is more than 1 pound per person per day.