Periodically, A Town Water Department Tests The The Drinking Water
This text snippet is about t-distribution tables, which are used in statistics for finding critical values of t. These tables list significance levels and degrees of freedom and can be used to calculate confidence intervals and perform hypothesis testing. They are also known as Student's t tables and provide information on the areas in the upper tail of a t-distribution. The table and its usage are further explained in a video and there are different versions of the table for different levels of confidence and significance.
To construct a 95% confidence interval for the mean lead level in water specimens from the town, we can use the t-distribution since the sample size is small (less than 30). The formula for the confidence interval in this case is:
[ \bar{x} \pm t \times \frac{s}{\sqrt{n}} ]
Where:
- (\bar{x}) is the sample mean
- (t) is the t-score for a 95% confidence level with 9 degrees of freedom (n-1)
- (s) is the sample standard deviation
- (n) is the sample size
Let's calculate the confidence interval using the given values:
- (\bar{x} = 2.4) mg/L
- (s = 1.8) mg/L
- (n = 10)
I'll calculate the t-score and then proceed with the confidence interval calculation.
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