Use a t-test to test the claim about the population mean p at the given level of significance a using the given sample statistics. Assume the population is normally distributed. Claim: u=51,300; a=0.10 Sample statistics: x=51,192, s= 3000, n 16 Click the icon to view the t-distribution table. What are the null and alternative hypotheses? Choose the correct answer below. Y A. H,: u=51,300 H u#51,300 O B. H, u#51,300 H p=51,300 O C. Ho us51,300 H p>51,300 O D. Ho u251,300 H u<51,300 What is the value of the standardized test statistic? The standardized test statistic is (Round to two decimal places as needed.)
Use a t-test to test the claim about the population mean p at the given level of significance a using the given sample statistics. Assume the population is normally distributed. Claim: u=51,300; a=0.10 Sample statistics: x=51,192, s= 3000, n 16 Click the icon to view the t-distribution table. What are the null and alternative hypotheses? Choose the correct answer below. Y A. H,: u=51,300 H u#51,300 O B. H, u#51,300 H p=51,300 O C. Ho us51,300 H p>51,300 O D. Ho u251,300 H u<51,300 What is the value of the standardized test statistic? The standardized test statistic is (Round to two decimal places as needed.)
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![**Using a t-Test to Evaluate a Claim About the Population Mean**
To assess a claim about a population mean \( \mu \) at a given significance level (\( \alpha = 0.10 \)), we use a t-test. Here is the information given for this problem:
- **Claim:** \( \mu = 51,300 \)
- **Sample statistics:**
- Sample mean (\( \bar{x} \)): 51,192
- Sample standard deviation (\( s \)): 3000
- Sample size (\( n \)): 16
- **Assumption:** The population is normally distributed.
### Steps:
1. **Hypotheses Formulation**
Determine the null and alternative hypotheses from the given options:
- **Option A:**
- Null hypothesis (\( H_0 \)): \( \mu = 51,300 \)
- Alternative hypothesis (\( H_a \)): \( \mu \neq 51,300 \)
- **Option B:**
- Null hypothesis (\( H_0 \)): \( \mu \neq 51,300 \)
- Alternative hypothesis (\( H_a \)): \( \mu = 51,300 \)
- **Option C:**
- Null hypothesis (\( H_0 \)): \( \mu \leq 51,300 \)
- Alternative hypothesis (\( H_a \)): \( \mu > 51,300 \)
- **Option D:**
- Null hypothesis (\( H_0 \)): \( \mu \geq 51,300 \)
- Alternative hypothesis (\( H_a \)): \( \mu < 51,300 \)
The correct choice based on a two-tailed test for equality is **Option A**.
2. **Standardized Test Statistic**
Calculate the value of the standardized test statistic. The formula for the t-statistic is:
\[
t = \frac{\bar{x} - \mu}{s/\sqrt{n}}
\]
Substituting in the given values:
\[
t = \frac{51,192 - 51,300}{3000/\sqrt{16}}
\]
Calculate and round to two decimal places as needed.
### Additional Support
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Transcribed Image Text:**Using a t-Test to Evaluate a Claim About the Population Mean**
To assess a claim about a population mean \( \mu \) at a given significance level (\( \alpha = 0.10 \)), we use a t-test. Here is the information given for this problem:
- **Claim:** \( \mu = 51,300 \)
- **Sample statistics:**
- Sample mean (\( \bar{x} \)): 51,192
- Sample standard deviation (\( s \)): 3000
- Sample size (\( n \)): 16
- **Assumption:** The population is normally distributed.
### Steps:
1. **Hypotheses Formulation**
Determine the null and alternative hypotheses from the given options:
- **Option A:**
- Null hypothesis (\( H_0 \)): \( \mu = 51,300 \)
- Alternative hypothesis (\( H_a \)): \( \mu \neq 51,300 \)
- **Option B:**
- Null hypothesis (\( H_0 \)): \( \mu \neq 51,300 \)
- Alternative hypothesis (\( H_a \)): \( \mu = 51,300 \)
- **Option C:**
- Null hypothesis (\( H_0 \)): \( \mu \leq 51,300 \)
- Alternative hypothesis (\( H_a \)): \( \mu > 51,300 \)
- **Option D:**
- Null hypothesis (\( H_0 \)): \( \mu \geq 51,300 \)
- Alternative hypothesis (\( H_a \)): \( \mu < 51,300 \)
The correct choice based on a two-tailed test for equality is **Option A**.
2. **Standardized Test Statistic**
Calculate the value of the standardized test statistic. The formula for the t-statistic is:
\[
t = \frac{\bar{x} - \mu}{s/\sqrt{n}}
\]
Substituting in the given values:
\[
t = \frac{51,192 - 51,300}{3000/\sqrt{16}}
\]
Calculate and round to two decimal places as needed.
### Additional Support
For further assistance, options such as "Help me solve this," "View an example," and "Get more
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