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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.
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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