1) A random sample of 50 helmets was subjected to quality control testing. It wa
ID: 3371147 • Letter: 1
Question
1) A random sample of 50 helmets was subjected to quality control testing. It was determined that 18 of those helmets did not meet the outgoing inspection requirements. Calculate a 95% upper bound on the true proportion of the helmets that would not meet the quality control testing. If using Minitab, use the normal approximation method.
2) For the same data in the previous question, calculate a 95% two-sided confidence interval. For this answer, just list the upper bound.
3) Is the answer for the upper bound in question 15 the same as that in question 14. If not, why?
A) They are the same because the p values are the same
B) They are the same because they are both upper bounds for the same data
C) They are different because the p values are different
D) They are not the same because a different z value is used
Explanation / Answer
Ans:
sample proportion=18/50=0.36
1)z value for upper bound=1.645 (i.e. upper tailed)
95% upper bound on true proportion
=0.36+1.645*sqrt(0.36*(1-0.36)/50)
=0.36+0.112
=0.472
2)z value for two sided CI=1.96 (i.e. two tailed)
95% confidence interval for true p
=0.36+/-1.96*sqrt(0.36*(1-0.36)/50)
=0.36+/-0.133
Upper bound=0.36+0.133=0.493
3) They are not the same because a different z value is used
Option D is correct.
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