A random sample of 60 suspension helmets used by motorcycle riders and automobile race-car drivers was subjected to an impact test, and on 16 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 60 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?

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kalsoomtahir1 kalsoomtahir1 · Answer 1 · 2019-12-10T00:35:27+01:00

Answer:

a)0.154<p<0.48[

b)n≅ 6.57

c)n=2401

Step-by-step explanation:

n = 60

Sample proportion = p = 16/60 = 0.266

a) Find a 95% two-sided confidence interval on the true proportion of helmets

90 % confidence interval fro population is

[tex]p +- z0.05/2 * \sqrt{p(1-p)/n}[/tex]

[tex]0.154<p<0.48[/tex]

hence population proportion lies in the confidence interval

b) helmets must be tested to be 95% confident

point of estimates i s- 0.266

Margin of error = 0.02

[tex]ME=z0.05/2*\sqrt{p(1-p)n}[/tex]

after putting values we get

n = 6.56

n≅ 6.57

c)large must the sample be

The sample is calculted as

[tex]n=(z0.025/E)^{2} 1/4[/tex]

[tex]n=(1.96/0.02)^{2} 1/4[/tex]

n=2401