A study was conducted at the University of Waterloo on the impact characteristics of football helmets used in competitive high school programs.There were three types of helmets considered,classified according to liner type: suspension,padded-suspension,and padded.In the study,a measurement called the Gadd Severity Index (GSI)was obtained on each helmet,using a standardized impact test.A helmet was deemed to have failed if the GSI was greater than 1200.Of the 81 helmets tested,29 failed the GSI 1200 criterion.Assume that the suspension helmets tested were selected at random.What are the point estimates of the proportion of suspension helmets that fail and the standard error of the estimate,respectively?
A)0.36;0.0028
B)0.64;0.053
C)0.36;0.053
D)0.64;0.0028
E)0.36;0.089

Question

Quizplus · Accepted Answer

The point estimate of the proportion of suspension helmets that fail is the number of helmets that failed (29) divided by the total number of helmets tested (81), which is 29/81 = 0.358, rounded to 0.36. The standard error (SE) of the proportion is calculated using the formula SE = sqrt[p(1-p)/n], where p is the proportion of failures (0.36), and n is the total number of helmets (81). Plugging the numbers in gives SE = sqrt[0.36*(1-0.36)/81] = 0.053.

A Study Was Conducted at the University of Waterloo on the Impact