Question

Penny Weights, use the weights of the post 1983 pennies to construct a 98% confidence interval estimate of the standard deviation of the weights of all post-1983 pennies. S=0.0165 n=37. Find confidence interval. a. 0.01231 < Ï < 0.2111 b. 0.01239 < Ï < 0.02111 c. 0.1391 < Ï < 0.2311 d. 0.001219 < Ï < 0.002111

Answer 1

c. 0.1391 < Ï < 0.2311

Explanation:

The formula for Confidence Interval is given as:

Mean ± z × Standard deviation/√n

Z score for 98% confidence interval = 2.326

Mean = Significance level = 100% - 98%

= 2% = 0.02

Standard deviation = S=0.0165

n= 37

Hence,

Confidence Interval =

0.02 ± 2.326 × 0.0165/√37

0.02 ± 0.0063094687

Confidence Interval

0.02 - 0.0063094687

= 0.1391

0.02 ± 0.0063094687

= 0.2311

Hence, the Confidence Interval = (0.1391, 0.2311)

= c. 0.1391 < Ï < 0.2311