In a sample of 80 light bulbs, the mean lifetime was 1217 hours with a standard deviation of 52 hours. a) Find a 95% confidence interval for the mean lifetime of this type of light bulb. b) Find a 98% confidence interval for the mean lifetime of this type of light bulb. c) An engineer claims that the mean lifetime is between 1208 and 1226 hours. With what level of confidence can this statement be made? d) How many light bulbs must be sampled so that a 95% confidence interval will specify the mean lifetime to within ±8 hours? e) How many light bulbs must be sampled so that a 98% confidence interval will specify the mean lifetime to within ±8 hours?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...