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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 u = 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 II:u # 5 cm. %3D

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 u = 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 II:u # 5 cm. %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 u = 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.
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 u = 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.
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