The lifetime (in years) of a laptop is known to be normally distributed with unknown mean lifetime µ and σ = = 0.5 year. A random sample of 25 laptops has an average lifetime of x = 3.2 years. (a) Construct a 95% two-sided confidence interval on the mean lifetime. (b) Construct a 95% lower-confidence bound on the mean lifetime. (c) Construct a 90% and 99% two-sided confidence interval on the mean lifetime and compare the width of these confidence intervals to the width in (a). What conclusion can you draw from this comparison?
The lifetime (in years) of a laptop is known to be normally distributed with unknown mean lifetime µ and σ = = 0.5 year. A random sample of 25 laptops has an average lifetime of x = 3.2 years. (a) Construct a 95% two-sided confidence interval on the mean lifetime. (b) Construct a 95% lower-confidence bound on the mean lifetime. (c) Construct a 90% and 99% two-sided confidence interval on the mean lifetime and compare the width of these confidence intervals to the width in (a). What conclusion can you draw from this comparison?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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
Transcribed Image Text:The lifetime (in years) of a laptop is known to be normally
distributed with unknown mean lifetime and σ = 0.5 year. A random
sample of 25 laptops has an average lifetime of = 3.2 years.
(a) Construct a 95% two-sided confidence interval on the mean lifetime.
(b) Construct a 95% lower-confidence bound on the mean lifetime.
(c) Construct a 90% and 99% two-sided confidence interval on the mean
lifetime and compare the width of these confidence intervals to the
width in (a). What conclusion can you draw from this comparison?
(d) Suppose that we want the margin of error on mean lifetime to be 0.1
year at 95% confidence. What sample size should be used?
Expert Solution

Step 1: (a) Identify the z-value for 95% confidence level:
Note:
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Using excel formula "=NORM.S.INV(1-(0.05/2))", the z-value for 95% confidence level is obtained as 1.96.
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