Question

4. 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, u, at which a particular type of metallic glass becomes brittle, 25 pieces of this metallic glass 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 following results were obtained: X 480°F and s 11°F Construct a 95% confidence interval to estimate . (20 points)

Answer 1

Answer:

The 95% confidence interval to estimate is 475.4592 to 484.5408

Step-by-step explanation:

Consider the provided information.

25 pieces of this metallic glass were randomly sampled from a recent production run.

That means the value of n is 25.

The degree of freedom is:

df = n-1

df = 25-1 = 24

X = 480°F and s = 11°F

We need to Construct a 95% confidence interval to estimate.

1-α=0.95

α=0.05

It is a two tail test with small sample size.

Determine the value of t by using Degrees of freedom and Significance level:

The required t value is 2.064

$95\% CI=\bar x\pm t_c\times \frac{s}{\sqrt{n}}$

Substitute the respective values as shown:

$95\% CI=480\pm 2.064\times \frac{11}{\sqrt{25}}$

$95\% CI=480\pm 4.5408$

$95\% CI=475.4592\ to\ 484.5408$

Hence, the 95% confidence interval to estimate is 475.4592 to 484.5408