Use the confidence level and sample data to find a confidence interval for estim
ID: 3132519 • Letter: U
Question
Use the confidence level and sample data to find a confidence interval for estimating the population . Round your answer to the same number of decimal places as the sample mean.
A random sample of 94 light bulbs had a mean life of 435 hours with a sample standard deviation of s = 25 hours. Construct a 90% confidence interval for the mean life, , of all light bulbs of this type.
430 hr < < 440 hr
427 hr < < 443 hr
425 hr < < 445 hr
431 hr < < 439 hr
430 hr < < 440 hr
427 hr < < 443 hr
425 hr < < 445 hr
431 hr < < 439 hr
Explanation / Answer
Note that
Margin of Error E = z(alpha/2) * s / sqrt(n)
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.05
X = sample mean = 435
z(alpha/2) = critical z for the confidence interval = 1.644853627
s = sample standard deviation = 25
n = sample size = 94
Thus,
Margin of Error E = 4.241342445
Lower bound = 430.7586576
Upper bound = 439.2413424
Thus, the confidence interval is
( 431 , 439 ) [ANSWER, D]
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