# The city has asked schools to test water in their drinking taps for levels of lead

The city has asked schools to test water in their drinking taps for levels of lead. Below is a table of lead levels based on random sampling conducted in fours schools (measured in parts per billion). An ANOVA analysis was performed on the data.

a) Use the values from the ANOVA output above to determine if the data provide sufficient evidence to indicate a difference in mean levels of lead between the schools. Show your hypotheses. You will need to determine the missing values for the ANOVA output (those things indicated by ???).

b) Compare the mean lead levels in School B and School C. Use a 95% confidence interval.

**Solution: **(a) We need to test the following hypotheses:

_{}

First, the F-ratio is

_{}

The p-value for 3 and 15 degrees of freedom is *p* = 0.000. Since the p-value is less than the significance level, *we reject the null hypothesis of equal means.*

(b) We have the following table:

The 95% confidence interval for_{} is given by

_{}

where the pooled standard deviation is computed as

_{}

This means that the confidence interval is

_{}

This means that there is a probability of 0.95 that the interval_{} contains the actual value of_{}. This means that the mean of school B is significantly higher than the mean of school C.

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