### How large must the sample be if we wish to be at least

Assignment Help Civil Engineering
##### Reference no: EM13544588

A random sample of 50 suspension helmets used by motorcycle riders and automobile race- car drivers was subjected to an impact test, and on 18 of these helmets some damage was observed.

(a) Test the hypothesis, H0: p = 0.3 versus H1: p > 0.3 with a = 0.05.

(b) Find the P-value for this test.

(c) Find a 95% two-sided traditional CI on the proportion of helmets of this type that would show damage from this test. Explain how this confidence interval can be used

to test the hypothesis in part (a).

(d) Using the point estimate of p obtained from the preliminary sample of 50 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?

(e) 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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