Question

A random sample of 16 pigs showed an average increase of weight of 20 kg when a new diet is administered. Assuming

that the increase in weight is normal with variance 4, find 95% confidence interval for average increase in weight due to

new diet. ( ) ( ) )

Answer 1

The critical value for $\alpha = 0.05$ is $z_c = z_{1-\alpha/2} = 1.96.$

The corresponding confidence interval is computed as shown below:

$$CI=(\bar{x}-z_c\times\dfrac{\sigma}{\sqrt{n}}, \bar{x}+z_c\times\dfrac{\sigma}{\sqrt{n}})$$

$$=(20-1.96\times\dfrac{4}{\sqrt{16}}, 20+1.96\times\dfrac{4}{\sqrt{16}})$$

$$=(18.04, 21.96)$$

Therefore, based on the data provided, the 95% confidence interval for the population mean is $18.04 < \mu < 21.96,$ which indicates that we are 95% confident that the true population mean $\mu$ is contained by the interval $(18.04, 21.96).$