Stats study questions

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Stats study questions
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2015-02-11 23:45:13
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  1. What is the difference between a sample and a population? Give an example of each. In what circumstances are a population and sample the same?
    A population is a collection of data whose properties you wish to understand. The population is the complete collection to be studied, which contains all observations of interest. A sample is a part of the population of interest, a sub-collection selected from a population. An example of a population is all of a store’s customers; an example of a sample relating to this population would be 100 randomly selected customers. A population and sample are the same when all observations in the population are used in our analysis.
  2. US zipcodes
    qualitative, nominal
  3. Canadian postal codes
    qualitative nominal
  4. Year (eg. 2015)
    quantitative, interval
  5. Assets per employee
    quantitative, ratio
  6. The FIFA 2015 Women’s World Cup will be played in Canada next summer. The group stage of the tournament will feature 24 teams divided into 6 groups of 4 teams each. a. If teams are put into groups using a completely random draw, how many unique groups of four teams are possible?
    combination

    24C4
  7. How many different ways can the letters P Q R and S be arranged?
    Permutation









    • he answer is 4! = 24.
    • This is because there are four spaces to be filled: _, _, _, _
    • The first space can be filled by any one of the four letters. The second space can be filled by any of the remaining 3 letters. The third space can be filled by any of the 2 remaining letters and the final space must be filled by the one remaining letter. The total number of possible arrangements is therefore 4 × 3 × 2 × 1 = 4!
  8. In how many ways can the letters in the word: STATISTICS be arranged?
    10!
  9. There are 10 balls in a bag numbered from 1 to 10. Three balls are selected at random. How many different ways are there of selecting the three balls?
    10C3
  10. If the order doesn't matter, it is a
    Combination
  11. If the order does matter it is a
    Permutation.
  12. what order could 16 pool balls be in?
    16!
  13. How do you determine the number of classes needed when classifying data? (ie housing data?)
    2^k>N

    • So log(2^k)>Log(55)
    • so k log(2) > log 55
    • K> log(55)/log(2)

    Remember K must be GREATER then this number
  14. Less than type cumulative frequency
    The total frequencies of a particular class and all classes prior to that particular class is called the Less than type cumulative frequency of that class or simply the Cumulative frequency of that class.
  15. When is there no mode?
    The mode is the most frequently occurring measurement. This data has no repeated measurements, and hence has no mode.
  16. How do you determine expected value?
    sum the probability*value of each opportunity
  17. How do you calculate variance?
    sum of all ....(x - mean)^2
  18. when calculating expected profit... remember to..
    subtract expenses from revenue!!
  19. The customer service department for a cell phone company claims that 90% of all customer complaints are resolved to the satisfaction of the customer during after filing a complaint with a customer service manager. A random sample of 12 customers who have filed complaints is selected.
    This is a binomial distribution, with n=12 and p=0.9. You can calculate these probabilities either from a binomial table, or with the binomial formula. I used the table. If you used the formula, your answers may have more decimal places, depending on where you rounded, this is totally fine.
  20. A coffee shop manager wishes to provide prompt service for customers at the drivethrough window. The coffee shop can currently serve up to 10 customers in a 15-minute period without significant delay. The average arrival rate is 7 customers per 15-minute period.
    • Poisson distribution
    •  probability that exactly 10 customers will arrive in a particular 15-minute period.
  21. Suppose a committee of five people is to be selected at random from a group of eight women and seven men. Let x equal the number of women on the chosen committee.
    a. What probability distribution do you think best describes x?
    There are two possible outcomes (male or female), sampling is without replacement and thus not independent, and the sample (n=5) is greater than 5% of the population (N=15). These are characteristics of a hypergeometric distribution.
  22. The average number of homes sold by the Acme Realty company is 2 homes per day. What is the probability that exactly 3 homes will be sold tomorrow?
    Poisson...

    μ = 2; since 2 homes are sold per day, on average.x = 3; since we want to find the likelihood that 3 homes will be sold tomorrow.e = 2.71828; since e is a constant equal to approximately 2.71828
  23. for any normally distributed population, the sampling distribution of the sample mean
    will also be normally distributed and the question indicates that the population of monthly returns is normally distributed.
  24. if the population was not normally distributed
    The population of all sample means may not be normally distributed, because with n=10, the central limit theorem does not apply.
  25. (i) If we select 100 persons out of 25,000 registered voters and question them about
    candidates and issues, the 100 persons are referred to as the population.
    false.
  26. (ii) The order that runners finish in a race would be an example of continuous data.
    false
  27. Another name for inductive statistics is descriptive statistics.
    false
  28. Discrete data is
    counted,
  29. Continuous data is
    measured
  30. the number of students in a class
    discrete data ( you can't have half a student)
  31. the results of rolling 2 dice
    discrete data
  32. A dog's weight
    continuous data
  33. The length of a leaf
    continuous data
  34. name of your school
    Nominal data
  35. Nominal data
    Nominal basically refers to categorically discrete data 

    This one is easy to remember because nominal sounds like name(they have the same Latin root).
  36. ordinal data
    efers to quantities that have a natural ordering. The ranking of favorite sports, the order of people's place in a line, the order of runners finishing a race or more often the choice on a rating scale from 1 to 5. With ordinal data you cannot state with certainty whether the intervals between each value are equal.
  37. Likert scales
    ordinal data

    ordinal sounds like order.
  38. Interval data
    is like ordinal except we can say the intervals between each value are equally split. The most common example is temperature in degrees Fahrenheit. The difference between 29 and 30 degrees is the same magnitude as the difference between 78 and 79
  39. Temperature
    Interval data

    The most common example is temperature in degrees Fahrenheit. The difference between 29 and 30 degrees is the same magnitude as the difference between 78 and 79 (although I know I prefer the latter).
  40. Ratio data
    interval data with a natural zero point. For example, time is ratio since 0 time is meaningful. Degrees Kelvin has a 0 point (absolute 0) and the steps in both these scales have the same degree of magnitude.
  41. time
    ratio since 0 time is meaningful. Degrees Kelvin has a 0 point (absolute 0) and the steps in both these scales have the same degree of magnitude.
  42. If it isn't nominal
    then it's quantitative.
  43. What is a requirement of frequency tables?
    being mutually exclusive
  44. Refer to the following price of jeans are recorded to the nearest dollar:
    The first two class midpoints are $62.50 and $65.50.
    What are the class limits for the third class?
    $67 and up to $70
  45. If a major sports star were to move into your neighbourhood, what would you expect to happen to the neighbourhood's "average" income?
    The mean income would increase significantly, but the median income would stay almost the same as before
  46. Simple random
    in statistics, a simple random sample is a subset of individuals (a sample) chosen from a larger set (a population). Each individual is chosenrandomly and entirely by chance, such that each individual has the same probability of being chosen at any stage during the sampling process, and each subset of k individuals has the same probability of being chosen for the sample as any other subset of k individuals.[1] This process and technique is known as simple random sampling, and should not be confused with systematic random sampling. A simple random sample is an unbiased surveying technique.
  47. Stratified random sample
    In statistical surveys, when subpopulations within an overall population vary, it is advantageous to sample each subpopulation (stratum) independently. Stratification is the process of dividing members of the population into homogeneous subgroups before sampling. The strata should be mutually exclusive: every element in the population must be assigned to only one stratum. The strata should also be collectively exhaustive: no population element can be excluded. Then simple random sampling or systematic sampling is applied within each stratum. This often improves the representativeness of the sample by reducing sampling error. It can produce a weighted mean that has less variability than the arithmetic mean of asimple random sample of the population.
  48. Cluster Sampling
    Cluster sampling is a sampling technique used when "natural" but relatively homogeneous groupings are evident in a statistical population. It is often used in marketing research. In this technique, the total population is divided into these groups (or clusters) and a simple random sample of the groups is selected. Then the required information is collected from a simple random sample of the elements within each selected group. This may be done for every element in these groups or a subsample of elements may be selected within each of these groups. A common motivation for cluster sampling is to reduce the total number of interviews and costs given the desired accuracy. Assuming a fixed sample size, the technique gives more accurate results when most of the variation in the population is within the groups, not between them.
  49. Systematic sampling
    Systematic sampling is a statistical method involving the selection of elements from an ordered sampling frame. The most common form of systematic sampling is an equal-probability method. In this approach, progression through the list is treated circularly, with a return to the top once the end of the list is passed. The sampling starts by selecting an element from the list at random and then every kth element in the frame is selected, where k, the sampling interval (sometimes known as the skip): this is calculated as:[1]
  50. The standard error of the mean will vary according to the size of the sample that is in thedenominator. As the sample size n gets larger, the variability of the sample means gets
    smaller.
    true
  51. An accounting firm is planning for the next tax preparation season. From last year's returns,
    the firm collects a systematic random sample of 100 filings. The 100 filings showed an
    average preparation time of 90 minutes with a standard deviation of 140 minutes. What assumptions do you need to make about the shape of the population distribution of all possible tax preparation times to make inferences about the average time to complete a tax
    form?
    The shape of the population distribution does not matter.
  52. when all numbers are the same, the variance is
    zero
  53. Six basic colours are to be used in decorating a new condominium. They are to be applied to a unit in groups of four colours. One unit might have gold as the principal colour, blue as a complementary colour, red as the accent colour and touches of white. Another unit might have blue as the principal colour, white as the complimentary colour, gold as the accent colour and touches of red. (4 points)
    (a) If repetitions are permitted, how many different units can be decorated?
    • 6 choices each for four positions, how many total different arrangements are there?
    • Use the multiplication rule: 6*6*6*6 = 1296
    • 1296 different units
  54. Six basic colours are to be used in decorating a new condominium. They are to be applied to a unit in groups of four colours. One unit might have gold as the principal colour, blue as a complementary colour, red as the accent colour and touches of white. Another unit might have blue as the principal colour, white as the complimentary colour, gold as the accent colour and touches of red. If repetitions are not permitted, how many different units can be decorated?
    • 6P4 = 360
    • 360 different units.

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