You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=14  with meanm=90.8  and a standard deviation of sd=10.6.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

what is the p-value for this sample:
right tailed

Since the population standard deviation is unknown, you need to use a **t-test** for the hypothesis. The formula for the **t-test statistic** is:

\[
t = \frac{\bar{X} - \mu_0}{s / \sqrt{n}}
\]

Where:  
- \( \bar{X} = 90.8 \) (sample mean)  
- \( \mu_0 \) = hypothesized population mean (typically 0 or whatever value is relevant)  
- \( s = 10.6 \) (sample standard deviation)  
- \( n = 14 \) (sample size)  

If we assume \( \mu_0 = 0 \) (as is common when testing), the t-statistic becomes:

\[
t = \frac{90.8 - 0}{10.6 / \sqrt{14}}
\]

First, calculate the denominator:

\[
\frac{10.6}{\sqrt{14}} = \frac{10.6}{3.7417} \approx 2.833
\]

Now, calculate the t-statistic:

\[
t = \frac{90.8}{2.833} \approx 32.056
\]

So the **t-statistic** is:

\[
t = 32.056
\]

### Step 2: Calculate the p-value (right-tailed)

Since this is a **right-tailed test**, we need the p-value corresponding to the computed t-statistic with **n - 1 = 13** degrees of freedom. You can find this using a t-distribution table or statistical software.

Using a t-table:  
For **t = 32.056** with **13 degrees of freedom**, the p-value will be extremely small (near 0). In fact, for such a high t-value, the p-value is effectively:

\[
\text{p-value} \approx 0.000
\]

This means the result is highly significant.

---

Would you like me to go into further details or check your specific hypothesis value?  

Here are 5 related questions you may explore:  
1. How do you determine whether to use a t-test or z-test?  
2. What is the difference between one-tailed and two-tailed tests?  
3. How do degrees of freedom affect the shape of the t-distribution?  
4. What are Type I and Type II errors in hypothesis testing?  
5. How would the p-value change if it were a two-tailed test?  

**Tip**: Always report your hypothesis \(H_0\) and \(H_1\) clearly before conducting tests for clarity and reproducibility.

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=14 with mean m=90.8 and a standard deviation of sd=10.6. What is the test statistic for this sample? (Report answer accurate to three decimal places.) Test statistic = ? What is the p-value for this sample: right-tailed.

Learn how to calculate the test statistic and determine the p-value for a sample when the population standard deviation is unknown. This example uses a sample size of 14 with a mean of 90.8 and a standard deviation of 10.6, applying a right-tailed t-test with step-by-step calculations. Ideal for college-level statistics students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation