Basic Statistics20795 marksNumerical: confidence interval meanConfidence interval for population mean
The mass of vitamin E in a capsule manufactured by a certain drug company is normally distributed with standard deviation 0.042 mg. A random sample of 36 capsules was analyzed and the mean mass of vitamin E was found to be 5.12 mg. Calculate a symmetric 95% confidence interval for the population mea
The mass of vitamin E in a capsule manufactured by a certain drug company is normally distributed with standard deviation 0.042 mg. A random sample of 36 capsules was analyzed and the mean mass of vitamin E was found to be 5.12 mg. Calculate a symmetric 95% confidence interval for the population mean mass of vitamin E per capsule. [5]
- Population standard deviation: $\sigma = 0.042$ mg (known) - Sample size: $n = 36$ - Sample mean: $\bar{x} = 5.12$ mg - Confidence level: $95%$ - Distribution: Normal Since $\sigma$ is known and the population is normal, use the $z$-distribution: $$\text{CI} = \bar{x} \pm z{\alpha/2}\cdot\frac...