A random sample of 70 suspension helmets used by motorcycle riders and automobile race-car drivers was subjected to an impact test, and on 17 of these helmets some damage was observed. (a) Find a 95% two-sided confidence interval on the true proportion of helmets of this type that would show damage from this test. Round your answers to 3 decimal places.

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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A random sample of 70 suspension helmets used by motorcycle riders and automobile race-car drivers was subjected to an impact
test, and on 17 of these helmets some damage was observed.
(a) Find a 95% two-sided confidence interval on the true proportion of helmets of this type that would show damage from this test.
Round your answers to 3 decimal places.
<p<
(b) Using the point estimate of p obtained from the preliminary sample of 70 helmets, how many helmets must be tested to be 95%
confident that the error in estimating the true value of p is less than 0.02?
n =
(c) How large must the sample be if we wish to be at least 95% confident that the error in estimating p is less than 0.02, regardless of
the true value of p?
п
Transcribed Image Text:A random sample of 70 suspension helmets used by motorcycle riders and automobile race-car drivers was subjected to an impact test, and on 17 of these helmets some damage was observed. (a) Find a 95% two-sided confidence interval on the true proportion of helmets of this type that would show damage from this test. Round your answers to 3 decimal places. <p< (b) Using the point estimate of p obtained from the preliminary sample of 70 helmets, how many helmets must be tested to be 95% confident that the error in estimating the true value of p is less than 0.02? n = (c) How large must the sample be if we wish to be at least 95% confident that the error in estimating p is less than 0.02, regardless of the true value of p? п
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