Question

A random sample of 10 chocolate energy bars of a certain brand has, on average, 230 calories per bar, with a standard deviation of 15 calories. Construct a 99% confidence interval for the true mean calorie content of this brand of energy bar. Assume that the distribution of the calorie content is approximately normal.

Answer 1

The formula to calculate a confidence interval for a population mean is as follows:

$CI=\bar{x}\pm z\cdot\cfrac{s}{\sqrt{n}},$

where:

• $\bar{x}=230$ : sample mean
• z: the chosen z-value, for a 99% confidence interval z = 2.576
• $s=15$ :  sample standard deviation
• n = 10:  sample size.

So,

$CI=230 \pm 2.576\cdot\cfrac{15}{\sqrt{10}}=\\= 230\pm12.22=(217.78, 242.22).$