REI recently changed its return policy on hiking boots from exchanging boots after any time period to only exchanging in the first 24 months, because too many hikers were not returning the boots because of problems, but because they had worn out. REI wants to know how long hiking boots last on average. A shoe materials specialist said that shoes worn regularly wear out with a standard deviation of 7.4 months. If REI wanted to calculate a 95% confidence interval for the number of days that hiking boots last with a margin of error of ±1 month, how large a sample size would REI need to take?

Denisse Fitzpatrick

Denisse Fitzpatrick

Answered question

2022-09-27

REI recently changed its return policy on hiking boots from exchanging boots after any time period to only exchanging in the first 24 months, because too many hikers were not returning the boots because of problems, but because they had worn out. REI wants to know how long hiking boots last on average. A shoe materials specialist said that shoes worn regularly wear out with a standard deviation of 7.4 months.
If REI wanted to calculate a 95% confidence interval for the number of days that hiking boots last with a margin of error of ±1 month, how large a sample size would REI need to take?(answer n=211)

Answer & Explanation

Helena Bentley

Helena Bentley

Beginner2022-09-28Added 10 answers

Sample size = ( Z σ / E ) 2
Where,
Z is critical value at 95% confidence level.
σ is standard deviation
E is margin of error
= ( 1.96 7.4 / 1 ) 2
= 210.37
Sample size = 211 (Rounded up to next integer)

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