Question

Sample 8 of Problem 4-3 was analyzed seven times, with $\overline{\mathbf{x}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{52793}$and s=0.00007. Find the 99 % confidence interval for sample 8 .

Short answer

As a result, there is a confidence interval of $1.52793\pm 0.00010$for at a confidence level of 99 percent, sample 8 was chosen.

Step-by-step solution

Definition of confidence interval

• A confidence interval is the range of values we see in our sample and for which we expect to discover a value that accurately represents the population.

The table below summarises the values

Given: The ratio of isotopes${}^{69}Ga$ and${}^{71}Ga$ in sample 8 is equal to 1.52793, according to Problem 4-3 of Chapter 4 of the book. The table below summarises this value, as well as other given values from the problem:

Determine the sample 8, at 99% CI

For sample 8, a 99 percent confidence interval (Cl) is required.

Solution :The can be calculated for sample 8 by using t - 3.707 for 99 % a level of confidence with a number of degrees of freedom of 6:

$$\begin{gathered} CIfor\mu =\overrightarrow{x}\pm \frac{ts}{\sqrt{n}}99\% \\ CI=1.52793\pm \frac{\left(3.707\right)\left(0.00007\right)}{\sqrt{7}} \\ =-1.52793\pm 0.00010 \end{gathered}$$

As a result, there is a confidence interval of $-1.52793\pm 0.00010$for at a confidence level of 99 percent, sample 8 was chosen.