Section 6.3: Confidence Intervals for PopulationProportions 5. The new Twinkle b

Question

Section 6.3: Confidence Intervals for PopulationProportions

5.    The new Twinkle bulb is being developed tolast more than 1000 hours. A random sample of 100 of these newbulbs is selected from the production line. It was found that 48lasted more than 1000 hours. Find the point estimate for thepopulation proportion, the margin of error for a 95% confidence andthen construct to the 95% confidence interval for the populationproportion p. (References: example 1 - 3 page 334 -337, end of section exercises 13 – 20 on page 339- 340)

a.    Find the margin of error E. (2.5points)

      Round Eto three decimal places

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

Explanation / Answer

The new Twinkle bulb is being developed to last more than 1000hours. A random sample of 100 of these new bulbs is selected fromthe production line. It was found that 64 lasted more than 1000hours. Find the point estimate for the population proportion, themargin of error for a 95% confidence interval and then construct tothe 95% confidence interval for the population proportion. point estimate = (64/100) = 0.64 ------------------------------------ a. Find the margin of error E. E = 1.96*sqrt[0.64*0.36/100] = 0.0941.. ------------------------------------ b. Construct a 95% confidence interval for the populationproportion p of all Twinkle bulbs. 0.64 - 0.0941

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