EXAMPLE 16 $t$ intervals for $\mu$ using technology

For the breakfast cereal data in Example 14, construct a 99% confidence interval for the population mean sodium content, using the TI-83/84, Minitab, and SPSS.

Solution

We use the instructions provided in the Step-by-Step Technology Guide below. The sample size $n=16$ is not large (≤30), so it is necessary to check for normality. Figure 17 indicates acceptable normality.

The results for the TI-83/84 in Figure 19 display the 95% $t$ confidence interval for the population mean sodium content to be

They also show the sample mean $\overline{x}=185.9375$, the sample standard deviation $s=56.81017368$, and the sample size $n=16$.

The Minitab results are shown in Figure 20, providing the sample size $n\text{ = }16$, the sample mean $\overline{x}=185.9$, the sample standard deviation $s\text{ = }56.8$, the standard error (SE mean) 14.2, and the 95% $t$ confidence interval (155.7, 216.2).

The SPSS results are shown in Figure 21, providing the sample mean $\overline{x}=185.9375$, the standard error 14.20254, and the 95% $t$ confidence interval (155.6655, 216.2095).