Answer to Question #333767 in Statistics and Probability for Plangggg

Question

The mean water consumption of 10 students in a week is 28 liters with a standard deviation of 1.6 liters. Consider 95% confidence level, the upper limit is

Answer 1

The critical value for $\alpha = 0.05$ and $df = n-1 = 9$ degrees of freedom is $t_c = z_{1-\alpha/2; n-1} = 2.262156.$

The corresponding confidence interval is computed as shown below:

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

$$=(28-2.262156\times\dfrac{1.6}{\sqrt{10}}, 28+2.262156\times\dfrac{1.6}{\sqrt{10}})$$

$$=(26.85543, 29.14457)$$

The upper limit is 29.14457 liters.