In Problem 3.69 on page 156, you were introduced to teabag-filling operation. An important quality characteristic of interest for this process is the weight of the tea in the individual bag. The file Teabags contains an ordered array of the weight, in grams, of a sample of 50 tea bags produced during an 8-hour shift. a. Is there evidence that the mean amount of tea per bag is different from 5.5 grams? Use α = 0.01. b. Construct a 99% confidence interval estimate of the population mean amount of tea bag. Interpret this interval. c. Compare the conclusions reached in (a) and (b).
In Problem 3.69 on page 156, you were introduced to teabag-filling operation. An important quality characteristic of interest for this process is the weight of the tea in the individual bag. The file Teabags contains an ordered array of the weight, in grams, of a sample of 50 tea bags produced during an 8-hour shift. a. Is there evidence that the mean amount of tea per bag is different from 5.5 grams? Use α = 0.01. b. Construct a 99% confidence interval estimate of the population mean amount of tea bag. Interpret this interval. c. Compare the conclusions reached in (a) and (b).
Solution Summary: The author explains how to perform the t-test using Minitab.
In Problem 3.69 on page 156, you were introduced to teabag-filling operation. An important quality characteristic of interest for this process is the weight of the tea in the individual bag. The file Teabags contains an ordered array of the weight, in grams, of a sample of 50 tea bags produced during an 8-hour shift.
a. Is there evidence that the mean amount of tea per bag is different from 5.5 grams?
Use
α
=
0.01.
b. Construct a 99% confidence interval estimate of the population mean amount of tea bag. Interpret this interval.
c. Compare the conclusions reached in (a) and (b).
Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.
A well-known company predominantly makes flat pack furniture for students. Variability with the automated machinery means the wood components are cut with a standard deviation in length of 0.45 mm. After they are cut the components are measured. If their length is more than 1.2 mm from the required length, the components are rejected.
a) Calculate the percentage of components that get rejected.
b) In a manufacturing run of 1000 units, how many are expected to be rejected?
c) The company wishes to install more accurate equipment in order to reduce the rejection rate by one-half, using the same ±1.2mm rejection criterion. Calculate the maximum acceptable standard deviation of the new process.
5. Let X and Y be independent random variables and let the superscripts denote
symmetrization (recall Sect. 3.6). Show that
(X + Y) X+ys.
8. Suppose that the moments of the random variable X are constant, that is, suppose
that EX" =c for all n ≥ 1, for some constant c. Find the distribution of X.
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