Cholesterol is vital to human health and well being. It plays an important role in the structure, fluidity and permeability of the cell membrane, and helps synthesize vitamin D and various hormones. Although cholesterol is essential for human health, high levels of cholesterol in the blood stream can lead to damaged blood vessels and cardiovascular disease. The cholesterol level in mg/dl of a group of Canadian adults is assumed to be normally distributed.

1. Five individuals are randomly selected from this group.

Below are the measurements of their cholesterol levels: 120 116 130 132 111

Compute a 95% confidence interval for the mean cholesterol level.

2. Fifteen individuals are randomly selected from this group.

120 116 130 132 111 122 130 111 143 127 129 135 150 121 112.

Compute a 95% confidence interval for the mean cholesterol level.

3. Based on these two confidence interval constructions, what do you conclude