To find the standardized test statistic [tex]\( t \)[/tex] for the provided data, we need to follow these steps:
1. Identify the given values:
- Sample size [tex]\( n = 15 \)[/tex]
- Sample mean [tex]\( \bar{x} = 10.1 \)[/tex]
- Sample standard deviation [tex]\( s = 0.8 \)[/tex]
- Population mean under the null hypothesis [tex]\( \mu_0 = 9.8 \)[/tex]
- Significance level [tex]\( \alpha = 0.05 \)[/tex]
2. Write down the formula for the t-statistic:
[tex]\[
t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}
\][/tex]
3. Substitute the given values into the formula:
[tex]\[
t = \frac{10.1 - 9.8}{0.8 / \sqrt{15}}
\][/tex]
4. Calculate the denominator:
[tex]\[
\frac{0.8}{\sqrt{15}} \approx \frac{0.8}{3.872} \approx 0.2066
\][/tex]
5. Calculate the numerator:
[tex]\[
10.1 - 9.8 = 0.3
\][/tex]
6. Divide the numerator by the denominator:
[tex]\[
t = \frac{0.3}{0.2066} \approx 1.452
\][/tex]
7. Round the t-value to three decimal places:
[tex]\[
t \approx 1.452
\][/tex]
So, the standardized test statistic [tex]\( t \)[/tex] is approximately 1.452 when rounded to three decimal places.
Therefore, the correct answer is:
D. 1.452
