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Chapter 54: Problem 1

Calculate 95\% confidence limits. What are the \(95 \%\) confidence limits of a sample with a mean \(=24.7\), standard deviation \(=6.8\) and number of data values \(=16 ?\) (Express your answer to three significant figures.)

Short Answer

Expert verified
The 95% confidence limits for the given data are 21.38 and 28.02.

Step by step solution

01

Calculate the standard error

Firstly, we calculate the standard error, which is the standard deviation divided by the square root of the sample size. Therefore, Standard error \(= 6.8 / √16 = 1.7.\)
02

Calculate the margin of error

Once the standard error is obtained, we then proceed to calculate the margin of error, using the value Z_(α/2) for a 95% confidence interval. Therefore, Margin of error \(= 1.96 * 1.7 = 3.32.\)
03

Obtain the Confidence limits

Finally, we calculate the confidence limits which are the sample mean plus and minus the margin of error. Accordingly, Lower limit \(= 24.7 - 3.32 = 21.38\) and Upper limit \(= 24.7 + 3.32 = 28.02\). As a result, the 95% confidence limits are 21.38 and 28.02.

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Most popular questions from this chapter

Practise using a \(t\)-test. chemistry student measures the paracetamol concentration (mg \(\mathrm{g}^{-1}\) ) in tablets by two different analytical methods. Seven tablets from different batches were analysed to see whether the results obtained by the two methods differed. Carry out a \(t\)-test on the data and draw appropriate conclusions. Paracetamol concentration \(\left(\mathrm{mg} \mathrm{g}^{-1}\right)\) $$ \begin{array}{|l|c|c|c|c|c|c|c|} \hline \text { Method 1 } & 7.5 & 8.1 & 7.6 & 6.2 & 7.5 & 7.8 & 8.9 \\ \hline \text { Method 2 } & 5.6 & 7.5 & 8.2 & 6.7 & 3.5 & 6.5 & 5.9 \\ \hline \end{array} $$
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