Question

Use the confidence level and sample data to find the margin of error 18) Weights of eggs: 95% confidence, n-52,-. 1.78 oz. 18) 0-0.40 oz Use the given degree of confidence and sample data to construct a confidence interval for the population me that the population has a normal distribution 19)) 19) n 30, x-85.4, s -11.5,90 percent

Answer 1

18) The Zcritical (2 tail) for $\alpha$ = 0.05, is 1.96

$ME = Zcritical * \frac{\sigma}{\sqrt{n}} = 1.96 * \frac{0.4}{\sqrt{52}} = 0.109$

19) Although the population has a normal distribution, population standard deviation is unknown and n = 30 (not > 30), we use the t scores

The tcritical (2 tail) for $\alpha$ = 0.1, df = 29 is 1.6499

The Confidence Interval is given by $\bar{x} \pm$ ME, where

$ME = tcritical * \frac{s}{\sqrt{n}} = 1.699 * \frac{11.5}{\sqrt{30}} = 3.57$

The Lower Limit = 85.4 - 3.57 = 81.83

The Upper Limit = 85.4 + 3.57 = 88.97

The Confidence Interval is (81.83 , 88.97)

(If the CI rounded to 1 decimal place is required it is (81.8, 89.0)