Question

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

a) What is the point estimate of the he true proportion of helmets that would show damage from this test
b) Find a 95% two-sided confidence interval on the true proportion of helmets that would show damage from this test.
c) Using the point estimate of p from the 50 helmets, how many helmets must be tested to be 95% confident that the error in estimating p is less than 0.02?

Answer 1

atleast 2213

Explanation:

Sample size n = 50

Favouring for using helmets x = 18

Sample proportion = x/n = 0.36

a) Point estimate of the he true proportion of helmets that would show damage from this test = 0.35

b)
`p =0.36\\q = 0.64\\se = \sqrt{(pq)/(n) } =0.06789`

Confidence interval 95%

=
`(0.36-1.96*0.06789, 0.36+1.96*0.06789)\\=(0.2270, 0.4930)`

c) If margin of error is to be less than 0.02 we must have

1.96 * std error <0.02

Or
`1.96*\sqrt{(0.64*0.36)/(n) } <0.02\\0.48*1.96/0.02 <√(n) \\n>2212.76`

Sample size should be atleast 2213