https://file.aiquickdraw.com/mathbot/file/1727503160956eerl3694.jpg

Find the test statistic and round to two decimal places.

To find the test statistic for this hypothesis test, we use the formula for the two-sample t-test for independent samples:

\[
t = \frac{\bar{X}_1 - \bar{X}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}
\]

Where:
- \(\bar{X}_1 = 0.44\), \(s_1 = 1.04\), \(n_1 = 17\)
- \(\bar{X}_2 = 0.37\), \(s_2 = 1.27\), \(n_2 = 17\)

Let's compute the test statistic \( t \).The test statistic \( t \) is approximately \( 0.18 \) (rounded to two decimal places).

Would you like any additional details or have any questions?

Here are 5 related questions to explore further:

1. How do you determine the degrees of freedom for this t-test?
2. What is the critical t-value at a 0.01 significance level for this test?
3. How would the test conclusion change if the significance level was 0.05?
4. What is the interpretation of a two-tailed vs. one-tailed test in this context?
5. How can we use confidence intervals to test the same hypothesis?

**Tip:** Always ensure that the assumptions of the t-test are met before using it, such as normality and equal variance (if applicable).

Use a 0.01 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment (similar to a placebo). What are the null and alternative hypotheses? Find the test statistic and round to two decimal places.

Learn how to perform a hypothesis test using a two-sample t-test to compare the mean reduction in pain between a magnet treatment and a sham treatment. Given significance level of 0.01, sample means, and standard deviations, this problem walks you through the hypothesis setup and test statistic calculation.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation