A major grocery store chain is trying to cut down on waste. Currently, they get peaches from two different distributors, WholeFruits and GreenGrocer. Out of two large shipments, the manager randomly selects items from both suppliers and counts the number of items that are not sell-able due to bruising, disease or other problems. She then makes a confidence interval. Is there a significant difference in the quality of the peaches between the two distributors

Question

24-03-2022
Mathematics

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A major grocery store chain is trying to cut down on waste. Currently, they get peaches from two different distributors, WholeFruits and GreenGrocer. Out of two large shipments, the manager randomly selects items from both suppliers and counts the number of items that are not sell-able due to bruising, disease or other problems. She then makes a confidence interval. Is there a significant difference in the quality of the peaches between the two distributors

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Martebi Martebi · Answer 1 · 2022-04-05T16:00:12+02:00

There is a significant difference in the quality of the peaches between the two distributors because:

We are 95% confident that the proportion of non sell-able items for Whole Fruits is anywhere between 0.064 and 0.156 HIGHER than the proportion of non sell-able items for Green Grocer.

What does confidence interval of 95% mean?

A confidence interval is a term that connote an estimate (plus or minus) the variation that may be seen in that specific estimate.

A 95% confidence interval implies that if a person do a research such as (two different distributors, e.g. WholeFruits and GreenGroce) and took 100 different samples and then compute a 95% confidence interval for each sample, it therefore means that about 95 of the 100 confidence intervals will hold the true mean value (μ).

See options below

We are 95% confident that the proportion of non sell-able items for Whole Fruits is anywhere between 0.064 and 0.156 LOWER than the proportion of non sell-able items for Green Grocer.

We are 95% confident that the proportion of non sell-able peaches for Whole Fruits is about -0.064 and 0.156.

We are 95% confident that the proportion of non sell-able items for Whole Fruits is anywhere between 0.156 LOWER and 0.064 HIGHER than the proportion of non sell-able items for Green Grocer.

We are 95% confident that the proportion of non sell-able peaches from Whole Fruits is anywhere between 0.064 and 0.156.

We are 95% confident that the proportion of non sell-able items for Whole Fruits is anywhere between 0.064 and 0.156 HIGHER than the proportion of non sell-able items for Green Grocer.

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