Use the confidence level and sample data to find a confidence interval for estim

Question

Use the confidence level and sample data to find a confidence interval for estimating the population u. Round your answer to the same number of decimal places as the sample mean.

A random sample of 78 light bulbs had a mean life of x (bar) =423 hours with a standard deviation of 26 hours. Construct a 90% confidence interval for the mean life, u, of all light bulbs of this type.

a. 417 hr<u<429hr

b. 418hr<u<428hr

c. 415hr<u<431hr

d. 416hr<u<430hr

9. Use the given data to find the minimum sample size required to estimate the population proportion.

Margin of error: 0.03, confidence level: 99%; from a prior study, p(hat) is estimated by 0.13.

a. 483

b. 1,001

c. 834

d. 25

10. Use the given information to find the minimum sample size required to estimate an unknown population mean u.

How many women must be randomly selected to estimate the mean weight of women in one age group, We want 90% confidence that the sample mean is within 3.2lb of the population mean, and the population standard deviation is known to be 12 lb.

a. 40

b. 55

c. 37

d. 39

Explanation / Answer

a)

Z for 90% Confidence is:1.65

95% Ci is:

(423-(1.65*26/sqrt(78)),423+(1.65*26/sqrt(78)))

=(423-4.85,423+4.85)

=(418.14,427.85)

b)

Me=2.57*sqrt(p*(1-P)/n)

(0.03/2)^2=2.57*0.13*0.87/n

n=483

c)

1.65=3.2/12/sqrt(n)

n=39 nearly

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