Periodically, a town water department tests the the drinking water of homeowners

Question

Periodically, a town water department tests the the drinking water of homeowners for contaminants such as lead. The lead levels in water specimens collected for a sample of 10 residents of the town had a mean of 2.7 mg/L and a standard deviation of 1.5 mg/L. Complete parts a through c. a. Construct a 95% confidence interval for the mean lead level in water specimens from the town. Round to three decimal places as needed.) b. Interpret the interval in terms of this application. Choose the correct answer below ? A The water department is confident that 95% of the mean lead level in drinking water for all residents in the town is described by this interval O B The water department can be 5% confident that the mean lead level in drinking water for all residents in the town is within this interval. ° C. The water department can be 95% confident that the mean lead level in drinking water for all residents in the town is 2.7 mg. D. O E. The water department can be 95% confident that the mean lead level in drinking water for all The water department can be 95% confident that the mean lead level in drinking water for all in the town is outside this interval s in the town is within this interval c. The phrase "95% confidence interval" means that if many intervals were constructed using the same methods and with the same sample size then [ intervals would contain the true value of which of the following choices? % of these O A. Population mean O B. Standard deviation OC. Sample mean O D. Standard error

Explanation / Answer

a)

CI for 95%

n = 10

mean = 2.7

t-value of 95% CI = 2.2622

std. dev. = 1.5000

SE = std.dev./sqrt(n)

= 1.5/sqrt(10)

= 0.47434

ME = t*SE

= 2.2622*0.47434

= 1.07304

Lower Limit = Mean - ME = 2.7 - 1.07304 = 1.62696

Upper Limit = Mean + ME = 2.7 - 1.07304 = 3.77304

95% CI (1.627 , 3.773 )

b)

Option E

c)

Sample Mean (Option C)

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