Logic 101 Practice Test: Inductive Logic - Statistical Reasoning | Practice Test / Quiz / MCQs

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Logic 101 Practice Test: Inductive Logic - Statistical Reasoning

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Avg score: 50% • Most missed: “Suppose that the average price of a piece of jewelry at Henry's Jewelers is $200…”

Statistical reasoning is a theory that involves choosing and checking ingredients for a statistical problem. These ingredients include: data, a model, and a prior. Statistical reasoning involves making interpretations based on sets of data, graphical representations, and statistical summaries. It can involve connecting one concept to another, such as understanding the relationship between the mean and standard deviation in a distribution. Statistical reasoning can also involve learning to use statistics and/or probabilistic re-zoning to make decisions in situations where knowledge is... Show more

Statistical reasoning is a theory that involves choosing and checking ingredients for a statistical problem. These ingredients include: data, a model, and a prior.

Statistical reasoning involves making interpretations based on sets of data, graphical representations, and statistical summaries. It can involve connecting one concept to another, such as understanding the relationship between the mean and standard deviation in a distribution.
Statistical reasoning can also involve learning to use statistics and/or probabilistic re-zoning to make decisions in situations where knowledge is incomplete or the future unpredictable.

Some examples of statistical reasoning include:
Probability using counting methods
Conditional probability
Permutations and factorial notation
Modeling data with a line of best fit
Mutually exclusive and non mutually-exclusive events
Modeling data with a curve of best fit
Independent events

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Logic 101 Practice Test: Inductive Logic - Statistical Reasoning

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1. Suppose that the costs of operating a certain restaurant increase by the following amounts: food: 4%, labor: 5%, electricity: 3%, taxes: 2%, repairs and maintenance: 4%. By how much have the costs of operating the restaurant increased?

Less than 5%.The modal average of the increases for these five items.Less than 2%.More than 18%18%

2. Suppose a poll is taken to sample voter preferences in an upcoming presidential election. To conduct the poll, an interviewer standing on a street corner in the financial district of a large city asks questions of people as they pass by. What result would be expected from such a poll?

The responses would accurately predict the outcome of the electionThe responses would be biased in favor of the Democratic candidate.The people on the street corner would refuse to speak to the interviewer.The people interviewed would not be candid with their answers.The responses would be biased in favor of the Republican candidate.

3. Suppose that the price of crude oil, the primary raw material for gasoline, increases by 30 percent. Assuming everything else stays the same, by how much has the cost of producing gasoline increased?

Less than 30 percentMore than 35 percent.32 percent.30 percent.35 percent.

4. Suppose two simultaneous random surveys were taken of a mid sized city to determine public acceptance of a proposed ballot measure. Survey X covered 1000 voters, and Survey Y covered 2000 voters. How would you expect the surveys to compare for accuracy?

Survey Y is 4 times more accurate than Survey X.Survey Y is probably about one percentage point more accurate than Survey XThe two surveys are equally accurate.Survey Y is twice as accurate as Survey XThere is no way of knowing how the two surveys compare.

5. Suppose that the average price of a piece of jewelry at Henry's Jewelers is $200, and Mr. Smith wants to spend approximately that much for his wife's birthday gift. Under what circumstances can Mr. Smith be reasonably assured of a selection of jewelry in his price range?

The jeweler has a reputation for selling quality merchandise.The average is a mean.The average is a modal average.The pieces of jewelry are reasonably pricedThe average is a median.

6. In a normal distribution, the data represented are:

Random.Skewed away from the median point.Skewed toward the mean point.Shaped like a triangleTrustworthy.

7. Suppose that you want to buy a pair of size 9 shoes, and you are told that the average size of the shoes in Bob's Shoe Store are size 9. Under what circumstances is this information useful to you?

The average is a modal average.The shoes reflect the latest fashions.The average is a medianThe average is a mean.The standard deviation is relatively large.

8. Suppose that a poll is taken about how marriage partners relate to each other, and one of the questions asked is if the person being interviewed has ever lied to his/her spouse. Can the responses to this question be trusted?

Yes, because the question is very straightforward.Yes, because the vast majority of marriage partners do not lie to their spouseNo, because interviewers who have lied to their spouse would probably deny it.No, because the question is ambiguous.Yes, because most people are inclined to answer truthfully in a poll.

9. Suppose a poll is taken to determine voter attitude about increasing the state income tax in exchange for increased social services (including welfare). If the poll is confined primarily to the poorer neighborhoods of the state, what results can be expected?

The poll would be biased against an increase in the state income tax.The poll would be biased in favor of increased social services.The people would refuse to speak to the interviewer.The responses would accurately reflect the opinion of the state's populationThe people interviewed would not be candid with their answers.

10. Suppose that the costs of operating a factory that manufactures copper pipe increase by the following amounts: copper: 6%, labor: 5%, electricity: 4%, taxes: 2%, repairs and maintenance: 3%. By how much have the costs of manufacturing the pipe increased?

Less than 2%.6%Less than 6%20%4%

11. Suppose, to select a sample from a population of 3000 persons, the following procedure is followed. The names of the people are written on identical, square pieces of thin cardboard measuring one inch on a side, and these pieces of cardboard are then tumbled in a clothes dryer (with the heat shut off). After 30 minutes, a blindfolded person reaches in and withdraws a selected number of names. What can be said about this sample?

The sample is probably biased because the names on the top of the heap would be selected first.The sample is probably biased because people with shorter names would be selected first.The sample is probably biased because clothes dryers are not supposed to be used in collecting samples.The sample is probably biased because the names toward the front of the dryer would probably be selected first.The sample is almost certainly random

12. One of the problems with the Literary Digest poll taken prior to the 1936 presidential election was:

Many of the people in the population could not afford a telephone.Most people were not at home at the time the calls were madeThe sample size was too small.The population was too large.The responses were biased because of the way the questions were phrased.

13. In regard to the outcome of a poll, as the confidence level increases,

The margin of error increases.The standard deviation becomes greater.The more difficult it becomes to avoid atypical cases.The standard deviation becomes smaller.The margin of error decreases

14. In a poll about creating a publicly funded healthcare program, suppose the question is asked, 'Should free healthcare be given to people who are too lazy to work and who have never paid any taxes?' Can the answers to this question be trusted?

Yes, because most people are inclined to answer truthfully in a poll.No, because the question is biased in favor of a negative answer.Yes, because the phrasing of a question rarely affects the answer.Yes, if the poll is randomNo, because the question is ambiguous.

15. If the variance of a set of data is relatively large, then:

The standard deviation diverges from the variance.The sample does not accurately represent the population.Most of the data fall close to the mean pointThe data tend to be more spread out from the mean point.The population from which the data are extracted tends to be large.

16. One way that pictograms can distort a message is by:

Ignoring the visual effect of a three dimensional image.Using fluorescent colors to create the pictogram.Chopping off the bottom of the pictogramUsing pastel colors to create the pictogram.Blurring the lines of the pictogram.

17. Suppose a poll shows Smith leading Jones by 52 percent to 48 percent for U.S. Senate. What can be said about the results of this poll?

If the margin of error is ± 3 percent, then Jones is ahead of SmithIf the margin of error is more than ± 2 percent, then Jones might lead Smith.If the sample is random, then the results of the poll are unimpeachable.If the confidence level is 99 percent, then Smith is certainly ahead of Jones.If the margin of error is ± 1 percent, then Smith is certainly ahead of Jones.

18. Suppose that two sets of data conform to a normal probability distribution, and that the standard deviation of Set X is 2, while the standard deviation of Set Y is 4. Then,

Set X contains a larger amount of data than set Y.The curve for Set X is more flattened and spread out than the curve for Set Y.Set Y contains a larger amount of data than set XThe variance for both sets of data will be the same.The curve for Set Y is more flattened and spread out than the curve for Set X.

19. Range, variance, and standard deviation are measurements of:

Intensity.QuantityDispersion.Gradations of quality.Sampling error.

20. If the standard deviation of a set of data is relatively small, then:

The standard deviation diverges from the variance.The sample does not accurately represent the population.The data tend to be spread out from the median point.The population from which the data are extracted tends to be large.Most of the data fall close to the mean point

21. One way of exaggerating the apparent message conveyed by a bar graph is by:

Altering the horizontal scale while leaving the vertical scale as is.Printing the bars in different colorsNarrowing the width of the bars.Altering the vertical scale while leaving the horizontal scale as is.Altering both the horizontal scale and the vertical scale by the same amount.

22. Suppose you are the pilot of a small commercial airplane, and you want to ensure that the plane will carry the load. What statistic would be most useful to you?

The mean weight of the passengers.The standard deviation of the data representing the weight of the passengersThe modal weight of the passengers.The dispersion of the data representing the weight of the passengers.The median weight of the passengers.

23. Suppose a quality control inspector pulls every tenth can of soup from a conveyor belt to ensure that the cans are filled to capacity. How should this procedure be evaluated?

The procedure is defective because it fails to specify which can is selected first.The sample is not large enough for the kind of test being done.The procedure guarantees that the sample is a random sample.The procedure calls for an excessively large sampleThe sample may not be a random sample.

24. Suppose that for a large population, the margin of error of Poll A is 2%, and the margin of error of Poll B is 4%. Then,

The sample used in Poll A is much larger than the sample used in Poll BThe sample used in Poll A is slightly larger than the sample used in Poll BThe sample used in Poll B is much larger than the sample used in Poll AThe sample used in Poll B is slightly larger than the sample used in Poll AThe difference in sampling error is unrelated to the size of the samples

25. The range of a set of data is:

The difference between the median value and the mean valueThe difference between the modal value and the mean value.The difference between the largest and smallest values.A measure of how much the data differ from the mean value.A measure of how much the data differ from the median value.

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