SOLUTION: 5. The new Twinkle bulb is being developed to last more than 1000 hours. A random sample of 100 of these new bulbs is selected from the production line. It was found that 48 lasted

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Question 211863: 5. The new Twinkle bulb is being developed to last more than 1000 hours. A random sample of 100 of these new bulbs is selected from the production line. It was found that 48 lasted more than 1000 hours. Find the point estimate for the population proportion, the margin of error for a 95% confidence and then construct to the 95% confidence interval for the population proportion p.
a. Find the margin of error E. (2.5 points)
Round E to three decimal places

b. Construct a 95% confidence interval for the population proportion p of all Twinkle bulbs. (2.5 points)

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The new Twinkle bulb is being developed to last more than 1000 hours. A random sample of 100 of these new bulbs is selected from the production line. It was found that 64 lasted more than 1000 hours. Find the point estimate for the population proportion, the margin of error for a 95% confidence interval and then construct to the 95% confidence interval for the population proportion.
point estimate = (64/100) = 0.64
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a. Find the margin of error E.
E = 1.96*sqrt[0.64*0.36/100] = 0.0941..
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b. Construct a 95% confidence interval for the population proportion p of all Twinkle bulbs.
0.64 - 0.0941 < p < 0.64 + 0.0941
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Cheers,
Stan H.