<p>A random sample of 92 light bulbs had a mean life of x (with a line above it)

Question

<p>A random sample of 92 light bulbs had a mean life of x (with a line above it) = 425 hours with a standard deviation of &#963; = 2 hours.</p>
<p>a. What is the point estimate for the mean life, &#956;, of light bulbs of this type?</p>
<p>b. Calculate an interval estimate for the mean life, &#956;, of light bulbs of this type. In other words, construct a 95% confidence interval for the mean life, &#956;, of light bulbs of this type.</p>
<p>c. Write the confidence interval in terms of probability statement.</p>
<p>d. Interpret the confidence interval in words.</p>

Explanation / Answer

a. What is the point estimate for the mean life, of light bulbs of this type?

xbar=mean=425

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b. Calculate an interval estimate for the mean life, of light bulbs of this type. In other words, construct a 95% confidence interval for the mean life, of light bulbs of this type.

Given a=0.05, Z(0.025)=1.96 (check standard nomral table)

SO 95% CI is

xbar ± Z*s/n

--> 425 ± 1.96*2/sqrt(92)

--> ( 424.5913, 425.4087)

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d. Interpret the confidence interval in words.

We have 95% confidence that the mean life of light bulbs will be in the interval.

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