Question

For a random sample of 50 measurements on the breaking strength of cotton threads, the mean breaking strength was found to be 210 grams and the standard deviation 18 grams.
1. Obtain a confidence interval for the true mean breaking strength of cotton threads of this type with confidence coefficient 0.90.

Answer 1

Answer:

205.81 to 214.19

Step-by-step explanation:

Sample size (n) = 50

Sample mean weight (X) = 210 grams

Sample standard deviation (s) = 18 grams

Confidence coefficient (Z) at 90% = 1.645

The confidence interval for the true mean breaking strength of cotton threads of this type, at a 90% confidence level, is given by:

$CI=X \pm Z*\frac{s}{\sqrt n}\\CI=210 \pm 1.645*\frac{18}{\sqrt 50}\\CI = 210 \pm 4.19\\CI =205.81\ to\ 214.19$

The confidence interval is 205.81 grams to 214.19 grams.