Reference no: EM131013042
Look in the "big" yellow pages for your area (try to choose a book that represents a population of about 500,000 or so). Count the number of bakery entries. Respond to the following:
1. If it's assumed the area represented by these yellow pages is at least 500,000, do you think that the number of bakeries (12) sampled in our case study was large enough to be valuable in planning the new business?
2. Was there any indication in the case study that our sample was random?
3. The standard deviation is one of the most important concepts in the area of statistics. In your own words, define standard deviation. Give an example of how you have used the concept of standard deviation in your life.
4. Suppose you are a grocery store owner (perhaps next-door to the bakery). You order apples from two different vendors and pay the same per pound to each supplier. You evaluate the two shipments and find that a sample of 7 apples from supplier A weighs (in ounces) [12, 13,15, 10, 9, 11, 12]. The sample of 7 apples from supplier B weighs (in ounces) [11, 8, 12, 16, 7, 9, 17]. Without doing any calculations, tell us which supplier you'd rather use and why.
Reponed to the stunted-
1- Look in the "big" yellow pages for your area (try to choose a book that represents a population of about 500,000 or so). Count the number of bakery entries. Respond to the following:
If it's assumed the area represented by these yellow pages is at least 500,000, do you think that the number of bakeries (12) sampled in our case study was large enough to be valuable in planning the new business?
Using the following:
Atlanta Ga 2014 pop estimates 456,002 (https://www.census.gov/quickfacts/table/PST045215/1304000)
Yp.com using Atlanta City Hall zipcode 30303 for "bakeries"
https://www.atlantaga.gov/index.aspx?page=601
~349 results returned
No. assuming (probably incorrectly), but assuming that all 349 hits are valid bakeries, 12 shops is ~ 3% of the available market. The caveat being if she only expects to sell product in a smaller radius than the whole phone book it might be a much higher percentage. There are lots of additional factors like how far would one really drive to pick up bakery items? If the people work outside the area are they more likely to buy near their business or their home? If these 12 bakeries are within the expected market range for the new start up they obviously have more weight to their numbers than to be polling a whole city but it's still a small sample.
• Was there any indication in the case study that our sample was random?
The comment "I was able to reach..." suggests that out of a list from the yellow pages Carla tried for a larger sample and got a smaller one, but as for random - it may have felt random to her, but the yellowpages are normally alphabetical so I would say with the knowledge given of her procedure, no not random. If she used as I did, YP.com then they sort based on some relevance algorithm and may be influenced by tiered levels of advertising costs. YP.com can also sort by distance and alphabetically so she might have only heard from bakeries beginning with the first few letters of the alphabet or only polled those closest (or furthest) away from her. Unless all the phone numbers used were placed in a hat for example, they were not picked it true random form. Even then, if the sample isn't random, choosing randomly from a sorted sample isn't really random either.
• The standard deviation is one of the most important concepts in the area of statistics. In your own words, define standard deviation. Give an example of how you have used the concept of standard deviation in your life.
Standard deviation in improper statistical terms how far from the average units one is. In personal and very generalized use, the feeling of standard deviation is in play when I price shop for an item. Be it technology or toilet paper I "poll" common places I can pick up said item for their prices. I get a feel for market value and can see who sells higher or lower than that middle ground price. Figuring out a true deal is when a price is considerably lower than it's normally found at and again generally speaking, a few standard deviations less than the average price. For only a few cents/dollars there are other factors that play a role in where I ultimately buy the item, (do I need it now or can I wait for delivery? etc...), but when you know the normal costs for an item you know when it's a great buy, a good buy, or a only if I have to purchase.
• Suppose you are a grocery store owner (perhaps next-door to the bakery). You order apples from two different vendors and pay the same per pound to each supplier. You evaluate the two shipments and find that a sample of 7 apples from supplier A weighs (in ounces) [12, 13,15, 10, 9, 11, 12]. The sample of 7 apples from supplier B weighs (in ounces) [11, 8, 12, 16, 7, 9, 17]. Without doing any calculations, tell us which supplier you'd rather use and why.
As for apple shopping, firstly - this doesn't state the same apples were provided from each vendor. If I got Fuji apples from one and Red Delicious from another, I really don't like Red Delicious :) For the sake of argument, making the assumption they are the same apples, the range of values is smaller in apple vendor A from that of B. That says on one level the consistency is higher whereas B has a larger size variance, but using that as a criteria for apple selection seems completely subjective to my knowledge of apple purchases. I'm not sure you can draw any cost basis analysis from this question. There needs to be more information. Regardless of whether or not A's apples weigh more or less than B's apples, I'm paying the same per pound so ultimately it's a matter of what appears the freshest and most appetizing. I would assume taste tests are also in order from someone buying produce and I would go with the sweeter of the crops. If there is some hidden correlation of sweetness to size and smaller apples or larger apples are statistically better then we can make a choice on vendor but that's really reaching. How any of this ties into statistics I didn't follow....
2-
1. From Yellowpages.com, a search in the Charlotte, North Carolina area produced 223 bakeries. If only 12 bakeries were sampled, this would represent 5.4% of the area bakery population. This case study does not appear large enough to provide reliable data that is representative of the bakery population as a whole.
2. As Carla said she was able to reach 12 of the owners, this implies that her survey was voluntary, which is not random. Also, we do not know is her method for selecting the 12 bakeries, which could also impact the validity of her results. In addition, her method to determine what her hours of operation should be, consisted of surveying 100 people passing by her rented location. Although, these would be the people most likely to purchase goods from her location, her convenience sampling is not a random sample.
3. In my words, standard deviation is the difference between how much a set of information differs from what the average (mean) is. I use this all the time, especially when making large purchases. I am able to cheat a little because Consumer Reports has already done the testing, and cost approximations. I am able to quickly compare product specs, costs, and test results and compare it to similar products. It allows me to quickly see a large amount of information and easily see any deviations from how the average products performed or how much they cost. I also see this used frequently when shopping. I usually find myself saying "That is way too much to pay for that. You can get that cheaper on Amazon", or "That is way cheap. Get two." Unknowingly comparing the item's price deviation to that of Amazon, or another store.
4. If I was a grocer, I would rather use supplier A, as the range is ounces between apples is less. Where supplier A had a weight range from 15-9, supplier B's range is 17-7. Although I am paying the same per pound either way, as a business owner I want my products to be consistent. I would also want my projected costs to remain consistent to be able to forecast my expenses.