The amount of weight a high school student carries in his or her bookbag follows a normal distribution with a standard deviation of σ = 2 pounds. Suppose a random sample of 20 bookbags produced a mean of 13 pounds. Construct a 95% confidence interval to estimate the mean bookbag weight for all high school students.

Given Data :

Sample mean $(x \bar{)} = 13$

Population standard deviation $(σ) = 2$

Sample size $(n) = 20$

Confidence interval level $(C I) = 95$

The level of significance:

$α = 1 - 0.95 = 0.05$

The critical value:

$z_{c} = Z_{\frac{α}{2}} = Z_{\frac{0.05}{2}} = 1.96$

The confidence interval:

$C I = \overset{―}{x} \pm z_{c} \cdot \frac{σ}{\sqrt{n}} = 13 \pm 1.96 \cdot \frac{2}{\sqrt{20}} = (12.118, 13.882)$

adbhutah.com

Articles: 1282