First, let's define our null and alternative hypotheses: H0: μ = 5 (The mean amount of waste generated per adult in your community is equal to the national average of 5 pounds per day) H1: μ 0.10, so we fail to reject the null hypothesis. There is not enough evidence to conclude that the mean amount of waste generated per adult in your community is less than the national average of 5 pounds per day.

Question

First, let's define our null and alternative hypotheses:

H0: μ = 5 (The mean amount of waste generated per adult in your community is equal to the national average of 5 pounds per day)

H1: μ < 5 (The mean amount of waste generated per adult in your community is less than the national average of 5 pounds per day)

Next, we calculate the test statistic using the formula for a one-sample t-test:

t = (X̄ - μ) / (s/√n)

where:
X̄ = sample mean = 4.8
μ = population mean = 5
s = sample standard deviation = 1.2
n = sample size = 21

Substituting the values, we get:

t = (4.8 - 5) / (1.2/√21) = -0.7071

Next, we find the p-value. The p-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true. We look this up in a t-distribution table or use statistical software. For a one-tailed test with 20 degrees of freedom (n-1), the p-value associated with t = -0.7071 is approximately 0.2449.

Finally, we compare the p-value to the significance level (α = 0.10). If the p-value is less than α, we reject the null hypothesis. If the p-value is greater than α, we fail to reject the null hypothesis.

In this case, 0.2449 > 0.10, so we fail to reject the null hypothesis. There is not enough evidence to conclude that the mean amount of waste generated per adult in your community is less than the national average of 5 pounds per day.

Knowee AI · Accepted Answer