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Sagot :
Answer:
See below
Explanation:
Check One-Sample T-Interval Conditions
Random Sample? √
Sample Size ≥30? √
Independent? √
Population Standard Deviation Unknown? √
One-Sample T-Interval Information
- Formula --> [tex]CI=\bar{x}\pm t^*(\frac{S_x}{\sqrt{n}})[/tex]
- Sample Mean --> [tex]\bar{x}=390.25[/tex]
- Critical Value --> [tex]t^*=2.0096[/tex] (given [tex]df=n-1=50-1=49[/tex] degrees of freedom at a 95% confidence level)
- Sample Size --> [tex]n=50[/tex]
- Sample Standard Deviation --> [tex]S_x=30.5[/tex]
Problem 1
The critical t-value, as mentioned previously, would be [tex]t^*=2.0096[/tex], making the 95% confidence interval equal to [tex]CI=\bar{x}\pm t^*(\frac{S_x}{\sqrt{n}})=390.25\pm2.0096(\frac{30.5}{\sqrt{50}})\approx\{381.5819,398.9181\}[/tex]
This interval suggests that we are 95% confident that the true mean levels of lead in soil are between 381.5819 and 398.9181 parts per million (ppm), which satisfies the EPA's regulated maximum of 400 ppm.
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