Questions: As part of your work for an environmental group, you want to see if the mean amount of waste generated per adult in your community is less than the national average of 5 pounds per day. You take a simple random sample of 23 adults in your community and find that they average 4.6 pounds with a standard deviation of 1.1 pounds. Suppose you know the amount of waste generated per day follows a normal distribution. Test at 0.01 significance. Round answers to 4 decimal places. a. H0: Select an answer ✓ b. H1= Select an answer v ? ∨ c. Test Statistic: d. P-value: e. Select the Decision Rule: Select an answer f. There Select an answer ✓ enough evidence to conclude

As part of your work for an environmental group, you want to see if the mean amount of waste generated per adult in your community is less than the national average of 5 pounds per day. You take a simple random sample of 23 adults in your community and find that they average 4.6 pounds with a standard deviation of 1.1 pounds.

Suppose you know the amount of waste generated per day follows a normal distribution. Test at 0.01 significance. Round answers to 4 decimal places.
a. H0: Select an answer ✓
b. H1= Select an answer v ? ∨
c. Test Statistic:
d. P-value:
e. Select the Decision Rule: Select an answer
f. There Select an answer ✓ enough evidence to conclude

Transcript text: As part of your work for an environmental group, you want to see if the mean amount of waste generated per adult in your community is less than the national average of 5 pounds per day. You take a simple random sample of 23 adults in your community and find that they average 4.6 pounds with a standard deviation of 1.1 pounds. Suppose you know the amount of waste generated per day follows a normal distribution. Test at 0.01 significance. Round answers to 4 decimal places. a. $\mathrm{H}_{0}:$ Select an answer $\checkmark$ b. $\mathrm{H}_{1}=$ Select an answer $v$ ? $\vee$ c. Test Statistic: d. P-value: e. Select the Decision Rule: Select an answer f. There Select an answer $\checkmark$ enough evidence to conclude

Solution

Solution Steps

Step 1: Formulate Hypotheses

We are testing whether the mean amount of waste generated per adult in the community is less than the national average of 5 pounds per day. The hypotheses are:

Null Hypothesis ($H_0$): $\mu = 5$
Alternative Hypothesis ($H_1$): $\mu < 5$

Step 2: Calculate Standard Error

The standard error ($SE$) is calculated using the formula:

\[ SE = \frac{\sigma}{\sqrt{n}} = \frac{1.1}{\sqrt{23}} = 0.2294 \]

Step 3: Compute Test Statistic

The test statistic for a single-sample mean test is calculated as follows:

\[ t = \frac{\bar{x} - \mu_0}{SE} = \frac{4.6 - 5.0}{0.2294} = -1.7439 \]

Step 4: Determine P-value

For a left-tailed test, the p-value is the probability that the test statistic is less than or equal to the observed value. The p-value is:

\[ P = T(t) = 0.0476 \]

Step 5: Decision Rule

The significance level ($\alpha$) is 0.01. We compare the p-value to $\alpha$:

If $P < \alpha$, reject the null hypothesis.
If $P \geq \alpha$, fail to reject the null hypothesis.

Since $0.0476 \geq 0.01$, we fail to reject the null hypothesis.

Final Answer

There is not enough evidence to conclude that the mean amount of waste generated per adult in the community is less than the national average of 5 pounds per day. Therefore, we fail to reject the null hypothesis.

$\boxed{\text{Fail to reject } H_0}$

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