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Bolts are manufactured with a nominal length of 5 cm, and it is known from past experience that the variance of the lengths of such bolts is 0.05 cm2. A random sample of 10 bolts is taken from a box containing a large number of bolts, and their lengths (in cm) are found to be 5-68, 5-13, 5-82, 5-71, 5-36, 5-52, 5-29, 5-77, 5.45, 5-39. (a) Find 95% confidence limits for the mean length, u, of bolts in the box, stating clearly any assumptions made in deriving the limits. ... (b) Without doing a formal test of a hypothesis, discuss whether = 5 cm is a plausible hypothesis, given the result in part (a). (c) By looking only at the number of bolts, out of 10, whose lengths are greater than 5 cm, construct a formal test of the null hypothesis Ho: = 5 cm, against the alternative II₁:μ # 5 cm.

Bolts are manufactured with a nominal length of 5 cm, and it is known from past experience that the variance of the lengths of such bolts is 0.05 cm2. A random sample of 10 bolts is taken from a box containing a large number of bolts, and their lengths (in cm) are found to be 5-68, 5-13, 5-82, 5-71, 5-36, 5-52, 5-29, 5-77, 5.45, 5-39. (a) Find 95% confidence limits for the mean length, u, of bolts in the box, stating clearly any assumptions made in deriving the limits. ... (b) Without doing a formal test of a hypothesis, discuss whether = 5 cm is a plausible hypothesis, given the result in part (a). (c) By looking only at the number of bolts, out of 10, whose lengths are greater than 5 cm, construct a formal test of the null hypothesis Ho: = 5 cm, against the alternative II₁:μ # 5 cm.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Bolts are manufactured with a nominal length of 5 cm, and it is known from past experience that the variance of the lengths of such bolts is 0.05 cm². A random sample of 10 bolts is taken from a box containing a large number of bolts, and their lengths (in cm) are found to be 5-68, 5-13, 5-82, 5-71, 5-36, 5-52, 5-29, 5-77, 5.45, 5.39. (a) Find 95% confidence limits for the mean length, p, of bolts in the box, stating clearly any assumptions made in deriving the limits. (b) Without doing a formal test of a hypothesis, discuss whether = 5 cm is a plausible hypothesis, given the result in part (a). (c) By looking only at the number of bolts, out of 10, whose lengths are greater than 5 cm, construct a formal test of the null hypothesis Ho: μ = 5 cm, against the alternative II₁:μ #5 cm.
Transcribed Image Text:Bolts are manufactured with a nominal length of 5 cm, and it is known from past experience that the variance of the lengths of such bolts is 0.05 cm². A random sample of 10 bolts is taken from a box containing a large number of bolts, and their lengths (in cm) are found to be 5-68, 5-13, 5-82, 5-71, 5-36, 5-52, 5-29, 5-77, 5.45, 5.39. (a) Find 95% confidence limits for the mean length, p, of bolts in the box, stating clearly any assumptions made in deriving the limits. (b) Without doing a formal test of a hypothesis, discuss whether = 5 cm is a plausible hypothesis, given the result in part (a). (c) By looking only at the number of bolts, out of 10, whose lengths are greater than 5 cm, construct a formal test of the null hypothesis Ho: μ = 5 cm, against the alternative II₁:μ #5 cm.
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