Answer to Question #314730 in Statistics and Probability for wiwili

Question

A process has been developed that can transform ordinary iron into a kind of super iron called metallic glass. Metallic glass is three to four times stronger than the toughest steel alloys. To estimate the mean temperature at which a particular type of metallic glass becomes brittle, 20 pieces of this material were randomly sampled from a recent production run. Each piece was subjected to higher and higher temperatures until it became brittle. The temperature at which brittleness first appeared was recorded for each piece in the sample. The result suggests that the average temperature which brittleness first appeared is about 545 degrees Fahrenheit with a standard deviation of 27 degrees Fahrenheit. Calculate the length of the 95% confidence interval for the mean temperature at which a particular type of metallic glass becomes brittle.

Note: Round your answer to 4 decimal places.

Answer 1

$Confidence\,\,interval:\\\left( \bar{x}-\frac{s}{\sqrt{n}}t_{n-1,\frac{1+\gamma}{2}},\bar{x}+\frac{s}{\sqrt{n}}t_{n-1,\frac{1+\gamma}{2}} \right) \\The\,\,length:\\l=2\frac{s}{\sqrt{n}}t_{n-1,\frac{1+\gamma}{2}}=2\frac{27}{\sqrt{20}}\cdot 2.09030=25.2399$