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The lifetime (in hours) of a 60-watt light bulb is a random variable that has a Normal distribution with o = 30. A random sample of 25 bulbs put on test produced a sample mean lifetime of T = 1050. We want to construct a 95% confidence interval for the mean lifetime u. We use 1.96 as the critical value for the 95% confidence interval. If it were desired to have the length of a 95% confidence interval no larger than 14 hours, what is the sample size required to achieve this result? 17 18 70 71

Sagot :

a) 92% Confidence interval: (1027.5,1048.5)

b) Sample size = 100

What is Sample size?

The process of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. Any empirical study with the aim of drawing conclusions about a population from a sample must take into account the sample size as a crucial component.

We are given the following in the question:

Sample mean,  = 1038

Sample size, n = 25

Alpha, α = 0.08

Population standard deviation, σ = 30

a) 92% Confidence interval:

[tex]$\mu \pm z_{\text {critical }} \frac{\sigma}{\sqrt{n}}$[/tex]

Putting the values, we get,

[tex]$z_{\text {critical }}$[/tex] at [tex]$\alpha_{0.08}=\pm 1.75$[/tex]

[tex]$1038 \pm 1.75\left(\frac{30}{\sqrt{25}}\right)=1038 \pm 10.5=(1027.5,1048.5)$[/tex]

b) In order to reduce the confidence interval by half, we have to quadruple the sample size.

Thus,

Sample size [tex]$=25 \times 4=100$[/tex]

To learn more about Sample mean visit:https://brainly.com/question/14127076

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