Question

A chemist examines 25 geological samples for bromide concentration. The mean bromide concentration for the sample data is 0.502 cc/cubic meter with a standard deviation of 0.0313. Determine the 98% confidence interval for the population mean bromide concentration. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answer 1

Answer:

The critical value that should be used is T = 2.492.

The 98% confidence interval for the population mean bromide concentration is between 0.486 cc/m³ and 0.518 cc/m³

Step-by-step explanation:

We have the standard deviation for the mean, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 25 - 1 = 24

98% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.98}{2} = 0.99$. So we have T = 2.492, which is the critical value that should be used.

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 2.492\frac{0.0313}{\sqrt{25}} = 0.016$

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 0.502 - 0.016 = 0.486 cc/m³

The upper end of the interval is the sample mean added to M. So it is 0.502 + 0.016 = 0.518 cc/m³

The 98% confidence interval for the population mean bromide concentration is between 0.486 cc/m³ and 0.518 cc/m³