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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.

Question: Find the margin of error E.

Round E to three decimal places

Answer:

E = zc ãpq/n

= 1.96 ã(0.48 x 0.52)/100

= 0.098

Question: Construct a 95% confidence interval for the population proportion p of all Twinkle bulbs.

Answer:

0.48 - 0.098 < p < 0.48 + 0.098