Solved: Confidence Intervals. In Exercise, construct the

Chapter 7, Problem 21BSC

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QUESTION:

Lead in Medicine Listed below are the lead concentrations (in $\mu$ g / g ) measured in different Ayurveda medicines. Ayurveda is a traditional medical system commonly used in India. The lead concentrations listed here are from medicines manufactured in the United States. The data are based on the article “Lead, Mercury, and Arsenic in US and Indian Manufactured Ayurvedic Medicines Sold via the Internet,” by Saper et al., Journal of the American Medical Association, Vol. 300, No. 8. Use the sample data to construct a 95% confidence interval estimate of the mean of the lead concentrations for the population of all such medicines. If a safety standard requires lead concentrations less than 7 $\mu$ g / g , does it appear that the population mean is less than that level?

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$\mu{}$

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Questions & Answers

QUESTION:

Equation Transcription:

$\mu{}$

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ANSWER:

Answer:

Step 1 of 2

The sample data meet the loose requirement of having a normal distribution

SL. No	x	(x - $\overline{x}\ {)}^{2}$
1	3	64.8025
2	6.5	20.7025
3	6	25.5025
4	5.5	30.8025
5	20.5	89.3025
6	7.5	12.6025
7	12	0.9025
8	20.5	89.3025
9	11.5	0.2025
10	17.5	41.6025
Sum	110.5	375.725
Average	11.05

The sample mean of the variable is the sum of observed values in a data divided by the number of observations.

Mean $\overline{x}$ = $\frac{sum\ of\ all\ the\ observations}{total\ number\ of\ observations}$

= $\frac{110.5}{10}$

= 11.05

Standard deviation is calculated as the square root of average of squared deviations taken from actual mean. It is also called root mean square deviation.

$s\ =\ \sqrt{\frac{\sum\limits_{\ }^{\ }({x}_{i}\ -\ \overline{x}\ {)}^{2}}{n\ -\ 1}}$