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Name THQ 7 Boxes of cereal are labeled as containing 14 ounces. Following, are w

ID: 3067206 • Letter: N

Question

Name THQ 7 Boxes of cereal are labeled as containing 14 ounces. Following, are weights, in ounces, for a random sample of 12 boxes. It is reasonable to assume that the weights of all cereal boxes of this type have a normal distribution. 1. 14.02 | 13.97 | 14.11 14.12 . 14.1 14.0 14.15 13.97 14.05 14.04 14.11 14.12 a) Construct a 98% confidence interval for the mean weight. Show all three steps. b) What is the point estimate for the mean weight? c) What is the margin of error E for your interval? d) What is the standard error for X e) A sample of electronic components are to be tested to estimate the mean lifetime. The lifetimes have a normal distribution with a population standard deviation of 20 hours. Find the sample size needed so that a 90% confidence interval will have a margin of error of 3 hours. 26

Explanation / Answer

a)

CI for = 98%

n = 12

mean = 14.065

t-value of 98% CI = 2.7181

std. dev. = 0.0614

SE = std.dev./sqrt(n) = 0.01772

ME = t*SE = 0.04818

Lower Limit = Mean - ME = 14.01682

Upper Limit = Mean + ME = 14.11318

98% CI (14.0168 , 14.1132 )

b)

Point estimate for the mean weight = 14.065

c)

Margin of error = t*SE = 0.04818

d)

standard error = std.dev./sqrt(n) = 0.01772

e)

s = 20, ME = 3 , z value at 90% = 1.645

ME = z *s/sqrt(n)

3 = 1.645 * 20/sqrt(n)

n = 120.267 = 121