Accurate Miniatures
"Sampling Distributions and Estimation" A random sample of 10 miniature Tootsie Rolls was taken from a bag. Others
A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very precise balance. The results in grams were 3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.411 3.437 3.477 (a) Construction of 90 interval percent confidence the true mean weight. (B) What is the sample size would be necessary to estimate the actual weight of an error of ± 0.03 g with 90 percent confidence? (C) Discuss the factors that could cause variations in the weight of Tootsie Rolls during manufacture. (These data are from a project by MBA student Henry Scussel.) Tootsie "sampling distributions and estimation"
intervals confidence) are used to find an area in which we are 100 * (1 - α)% confident the true value of the parameter is the interval. To confidence interval to be valid, you must have data from a normal distribution, at least if you use the method here. If you have no normal data then this type of confidence interval is invalid. To lighten the notation I will use here. "T" the test statistic and "t_ (n-1)" is a random variable of Student with n - 1 degrees of freedom, for example, a random variable of Student 18 degrees of freedom is noted that t_18.For small confidence intervals around the sample mean that you have: xBar t ± * sx / sqrt (n) xBar where is the sample mean t is t - score n - 1 degrees of freedom such that α% of the data in the tails, ie P (| t_ (n-1) |> t) = α sx is the sample standard deviation n is the sample size The sample mean xbar The sx = 3.3048 SD = 0.1319889 The sample size n = 10 score t for a confidence interval is 0.9 t such that the score is 0.05 in each tail. t = 1.833113 The confidence interval is: (xbar - t * sx / sqrt (n), xbar + t * sx / sqrt (n)) (3.228289, 3.381311) b) Intervals of trust are used to find an area in which we are 100 * (1 - α)% confident the true value of the parameter is in between. For large confidence intervals of the sample average you: xBar ± sx * z / sqrt (n) where xBar is the sample mean z is the Zscore% for α data in the tails, ie P (| Z |> z) = α sx is the sample standard deviation n is the sample size to find the sample size required for a confidence interval of a given size, we we need only worry about the error term of the IC. We know that the interval is centered at xbar we must find the value of n such that sx * z / sqrt (n) = width. Z-score confidence interval 0.9 is the value of z such that 0.05 is in each tail of the distribution. z = 1.644854 The equation we must resolve is: z * sx / sqrt (n) = n = width (z * sx / width) ^ 2. n = (1.644854 * 0.1319889 / 0.03) ^ 2 = 52.3705 n Since n must be an integer value that we must take the limit of this solution. Always look on the ceiling, so that the size of the CI will be correct. n = 53 c) not to you, for most. mixing the dough, measuring machines, moisture in the plant, etc. ...
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