Chapter 9.3, Problem 82E

To determine

To construct: The 95% confidence interval for the population mean. Also, explain the additional information that is being provided by the confidence interval.

Answer to Problem 82E

The confidence interval is (297.46,300.61)

Explanation of Solution

Given:

The data set is:

299.4

297.7

301

298.9

300.2

297

Formula used:

The formula to compute the t -interval is:

  $CI=\overline{x}\pm t_{\alpha /2}\times \frac{s}{\sqrt{n}}$

Calculation:

The obtained output using Ti-83 plus calculator is:

From the above output, the 95% confidence interval is $\left(297.46,300.61\right)$ . It means that there are 95% chances that mean amount of bottle filled is between 297.46 and 300.61 ml. Here, 300 does lie in the computed confidence interval. Thus, there is sufficient evidence to conclude that mean amount of cola filled in all bottle is not different from 300 ml.