Dream Score Representative
Joined: 07 Oct 2021
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Re: Almost everyone purchases some snack foods. Data show that over the
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04 Jan 2022, 13:41
1.1) If a government with a population of 50 million households were considering a tax on all salty snacks on a per pound basis, select Fewer, if based on the information in the tabs, it can be reasonably expected that the listed tax rate per pound would generate fewer than 555 million dollars in revenue. Otherwise, select More.
From tab 3, we can see 99.2% of the population would purchase salty snacks and each household that purchased salty snacks would purchase 31.81 pounds on average. Thus, 50 million households would purchase \(50 \text{ million} * 99.2\% * 31.81 = 1577.776 \text{ million pounds}\) of salty snacks.
In order to general 555 millions of tax, we need a tax of \(\frac{555}{1577.776} = 35.18\%\). Thus the first two rows are Fewer, the last row is More.
1.2) The most reasonably inferred statement from the information in the tabs is that
The information is mostly found in tab 1 and tab 3, so focus on those tabs.
a. potato chips were the most popular type of chip in 1999
We can see 91.3% of households purchased potato chips from tab 3 but that does not mean potato chips are the most popular type. Maybe 95% of the households purchased corn chips as 95.5% of the population purchased some type of chips.
b. pretzels and microwave popcorn were less popular than potato chips in 1999
Pretzels and microwave popcorn are categorized in "other salty snacks", which 96.8% of households have purchased. Then it is possible that more households purchased pretzels and microwave popcorn, compared to the 91.3% potato chips.
c. pretzels and microwave popcorn were more popular than potato chips in 1999
We can use the reasoning in (a) to see this is not true.
d. there were approximately two people per household in 1999
Focus on tab 3. If we divide the average quantity purchased per household (2nd column) by per capital purchased (3rd column), we will get approximately 2 for each row.
e. taxes on salty snacks were more popular than other food taxes in 1999
We did not mention taxes in these tabs.
Therefore the answer to this question is D.
1.3) For each of the following, select Supported if it is a statistical statement supported by the information in Tab 2. Otherwise, select Not supported.
1) 70 pounds of salty snack consumption was more than two deviations from the mean salty snack consumption in 1999.
We are essentially asking if 70 is far enough away from the mean of the data. Observing tab 2, we cannot identify the mean of this plot due to the last bar of ">150." If we put extreme values in for that last bar, it is possible to raise the mean up to 70, so we cannot tell where the mean lies and it might just be near 70. Thus this statement is NOT SUPPORTED.
2) Approximately one-fifth of all households consumed 10 pounds or fewer of salty snacks in 1999.
Note how the prompt mentions the modal is 10-12 pounds, we can observe there are 6 bars before the highest bar. Thus the 1st bar represents the number of households who purchased 0 pounds, and we have 0-2, 2-4, ..., 8-10 for the next 5 bars. Adding those 6 bars up gives us roughly 20, which represents 20% of the households. Thus this statement is SUPPORTED.
3) The median range of salty snack consumption is approximately 70 pounds greater than the modal range of salty snack consumption.
The median range is the bar that contains the 50% cutoff of all households. Using the information from earlier, 0-12 pounds represents a total of 25% of the households. We look 5 bars further which represent 12-22, and they represent roughly 4% * 5 = 20% of the entire population which brings us up to 45% of the population. We can see the median is going to lie somewhere between 24~28 then. Thus this statement is NOT SUPPORTED.