[8 points] The charge-to-tap time (min) for a carbon steel in one type of open h

Question

[8 points] The charge-to-tap time (min) for a carbon steel in one type of open hearth furnace was determined for each heat in a sample of size 46, resulting in a sample mean time of 382.1 and a sample standard deviation of 31.5. Calculate a 99% confidence interval for true average chargeto-tap time showing steps as directed. Estimate: …………… Critical value: ………………….. Standard error: …………………… Margin of error: ………………………….. Lower limit: ……………. Upper limit: ……………….. Interval: ……………………………………

Interpret the interval: Interpret the confidence 99% Use calculator to compute the 99 confidence interval using T-distribution. Which interval is more accurate? Why?

Explanation / Answer

Answer to the question)

Given:

.

The point estimate is same as the sample mean = 382.1

Critical value of t for 99% confidence level , and df = (46-1 = 45) is 2.69

( refer to T table , or use excel command =T.INV.2T(0.01,45)

[in this formula 0.01 is the value of alpha

alpha = 1 - confidence level

alpha = 1 -0.99 =0.01]

.

Standard error = s / sqrt(n)

standard error = 31.5 /sqrt(46)

standard error = 4.644

.

Margin of error = t * Standard error

Margin of error = 2.69 * 4.644

Margin of error = 12.4925

.

Lower limit = Estimate - margin of error

Lower limit = 382.1 - 12.4925

Lower limit = 369.6075

.

Upper limit = Estimate + Margin of error

Upper limit = 382.1 + 12.4925

Upper limit = 394.5925

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