Question

based on this analysis, what can you conclude about the true inventory defect rate of storage type 1?

Answer 1

With a 95% confidence level, the best estimate of the true defect rate for storage type 1 is approximately between 2.95% and 3.01%.

How to calculate the confidence interval for the true defect rate

To calculate the confidence interval for the true defect rate of storage type 1, use the provided mean, standard deviation, and sample size.

Given information:

Mean (x) = 0.0298

Standard Deviation (σ) = 0.1701

Sample Size (n) = 5000

We can use the formula for the confidence interval for a proportion (defect rate) using the normal approximation:

Confidence Interval = x ± z *
`\sqrt(`(x * (1 - x)) / n)

Where:

x = sample mean

z = z-score corresponding to the desired confidence level (95% confidence level corresponds to z = 1.96)

n = sample size

Plugging in the values:

Confidence Interval = 0.0298 ± 1.96 *
`\sqrt(`(0.0298 * (1 - 0.0298)) / 5000)

Calculating the confidence interval:

Confidence Interval = 0.0298 ± 1.96 *
`\sqrt(`(0.0298 * 0.9702) / 5000)

Confidence Interval = 0.0298 ± 1.96 *
`\sqrt(`0.00002887036 / 5000)

Confidence Interval = 0.0298 ± 1.96 * 0.000134975

Confidence Interval = 0.0298 ± 0.0002646

Lower Bound = 0.0298 - 0.0002646

Lower Bound ≈ 0.0295 (or 2.95%)

Upper Bound = 0.0298 + 0.0002646

Upper Bound ≈ 0.0301 (or 3.01%)

Therefore, with a 95% confidence level, the best estimate of the true defect rate for storage type 1 is approximately between 2.95% and 3.01%.

Find complete question below

Let's analyze the inventory sampling data Amazon collected after the implementation of cardboard dividers. In particular, let's construct confidence intervals to estimate the true inventory defect rate for each of the three different storage types at the warehouse. One of these storage types uses the cardboard divider. Amazon sampled 5,000 observations from each of the three different storage types and recorded 1 if there was a defect in the bin and 0 if there was not. The mean defect rate and standard deviation for each storage type are provided below. Using a 95% confidence level, calculate your best estimate of the true defect rate of storage type 1.

Storage Type 1

mean= 0.0298

sd=0.1701

n= 5000

Storage Type 2

mean= 0.0326

sd=0.1776

n= 5000

Storage Type

mean= 0.0586

sd=0.2349

n= 5000

Lower Bound 2.51%

Upper Bound 3.45%