Question

Given a sample of 35, what is the sample standard deviation of a pair of jeans if the 90% confidence interval is [37.14, 42.86]

Answer 1

10.295

Explanation:

Using the value for calculating the confidence interval as given;

CI = xbar + Z*σ/√n

xbar is the mean = 37.14+42.86/2

xbar= 80/2

xbar = 40

Z is the z-score at the 90% confidence = 1.645

σ is the standard deviation

n is the sample size = 35

Given the confidence interval CI as [37.14, 42.86]

Using the maximum value of the confidence interval to get the value of the standard deviation, we will have;

42.86 = xbar + Z*σ/√n

42.86 = 40 + 1.645* σ/√35

42.86-40 = 1.645*σ/√35

2.86 = 1.645*σ/√35

2.86/1.645 = σ/√35

1.739 = σ/√35

1.739 = σ/5.92

σ= 1.739*5.92

σ = 10.295

Hence, the sample standard deviation of a pair of jeans is 10.295