**Part 2**
A test is run to answer the research question, ’Is the average relationship length equal to 38?’

Which test is correct to use, if we know the population standard deviation?

Answer 4 Question 2 z-testt-test

The test statistic is -1.36. This means that the difference between the sample mean and the possible population mean, as stated in the null hypothesis (i.e. 38), is:

Answer 5 Question 2 -1.36 times the standard deviation of the relationship length-1.36 times the standard error of the sample mean-1.96 times the standard deviation of the relationship length-1.96 times the standard error of the sample mean

The p-value of the test is 0.175. What is the decision of the test?

1. **Which test is correct to use if we know the population standard deviation?**

- The correct test to use when the population standard deviation is known is the **z-test**. The z-test is appropriate in this scenario because it allows us to compare the sample mean to the population mean when the population variance is known.

2. **Interpretation of the test statistic -1.36**

- The test statistic of **-1.36** means that the difference between the sample mean and the population mean (as stated in the null hypothesis, i.e. 38) is **-1.36 times the standard error of the sample mean**. This is because the z-test formula involves dividing the difference between the sample mean and the population mean by the standard error of the sample mean.

3. **What is the decision of the test with a p-value of 0.175?**

- Since the **p-value is 0.175**, it is higher than typical significance levels such as **0.05 or 0.01**. Therefore, the decision would be to **fail to reject the null hypothesis**. This means there is not enough evidence to conclude that the average relationship length is different from 38.

---

Do you have any further questions or need additional details? Here are five related questions:

1. How is the standard error of the sample mean calculated?
2. What are the assumptions of the z-test?
3. How would you interpret a p-value of 0.05?
4. What is the difference between a z-test and a t-test?
5. How does sample size affect the p-value in hypothesis testing?

**Tip**: Always check if the population variance is known when deciding between a z-test and a t-test!

A test is run to answer the research question, 'Is the average relationship length equal to 38?' Which test is correct to use if we know the population standard deviation? The test statistic is -1.36. This means that the difference between the sample mean and the possible population mean, as stated in the null hypothesis (i.e. 38), is -1.36 times the standard deviation of the relationship length or -1.36 times the standard error of the sample mean. The p-value of the test is 0.175. What is the decision of the test?

Understand how to test if the average relationship length equals 38 using the z-test. This page explains the use of the z-test when the population standard deviation is known, interpreting a test statistic of -1.36 and a p-value of 0.175. Learn about standard error, hypothesis testing, and decision-making in statistics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation