College

**Hypothesis Testing: Testing a Claim About a Mean**

**Question 3**

Given:
- Null hypothesis: [tex] H_0: \mu = 35.26 [/tex]
- Alternative hypothesis: [tex] H_1: \mu \neq 35.26 [/tex]
- Sample size: 36 subjects
- Sample mean: 35.9
- Sample standard deviation: 3.88

Calculate the test statistic, rounded to 2 decimal places.

[tex] t = \square [/tex]

Submit your answer in the box provided.

Answer :

To calculate the test statistic for this hypothesis testing question, follow these steps:

1. Identify the given information:
- Sample mean ([tex]\( \bar{x} \)[/tex]) = 35.9
- Sample size ([tex]\( n \)[/tex]) = 36
- Sample standard deviation ([tex]\( s \)[/tex]) = 3.88
- Population mean ([tex]\( \mu_0 \)[/tex]) = 35.26

2. Calculate the standard error of the sample mean:
The standard error (SE) is calculated using the formula:
[tex]\[
\text{SE} = \frac{s}{\sqrt{n}}
\][/tex]
Substituting the given values:
[tex]\[
\text{SE} = \frac{3.88}{\sqrt{36}} = \frac{3.88}{6} \approx 0.65
\][/tex]

3. Calculate the test statistic (t-value):
The formula for the t-value is:
[tex]\[
t = \frac{\bar{x} - \mu_0}{\text{SE}}
\][/tex]
Substituting the known values:
[tex]\[
t = \frac{35.9 - 35.26}{0.65} \approx \frac{0.64}{0.65} \approx 0.99
\][/tex]

4. Conclusion:
The test statistic, rounded to two decimal places, is [tex]\( 0.99 \)[/tex].

This provides the calculated t-value for the hypothesis test.

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