Statistics for Scientists and Engineers Final

1. 1An effective way to check a distributional assumption is to construct a [blank_start]probability plot[blank_end]

   1. Aprobability plot
2. 2Normal Probability Plots
   1) The n observations are ordered in [blank_start]increasing[blank_end] order
   2) An [blank_start]ordered number[blank_end] i = 1, 2, ..., n is assigned to each observation
   3) Using order numbers, the [blank_start]quantiles[blank_end] [blank_start](i-0.5)/n[blank_end] are calculated for n observations
   4) Each observation is plotted against their [blank_start]quantiles/percentiles[blank_end] found in the previous step
   
   Using the quantiles from step [blank_start]3[blank_end], the corresponding [blank_start]z-scores[blank_end] can also be found and then plotted versus the observations.

   1. Aincreasing
   2. Bdecreasing
   3. Crandom
   4. Dordered number
   5. Eprobability number
   6. Fimmediate number
   7. Gquantile number
   8. Hquantiles
   9. Ipercentiles
   10. Jtextiles
   11. K(i-0.5)/n
   12. L(n+0.5)/i
   13. M(i+0.5)/n
   14. N(n-0.5)/n
   15. Oquantiles/percentiles
   16. Pquantiles
   17. Qpercentiles
   18. Rorder numbers
   19. Sz-scores
   20. Tpercentiles
   21. Uprobabilities
   22. Vt-scores
   23. W1
   24. X2
   25. Y3
   26. Z4
3. 3If the plot is based on the [blank_start]correct[blank_end] distribution, the points in the plot will fall close to a [blank_start]straight[blank_end] line

   1. Acorrect
   2. Bstraight
4. 4If the pattern of the points in the plot is reasonably close to a straight line, then the data appears to have come from a population that has a [blank_start]normal[blank_end] distribution

   1. Anormal
5. 5A _______ is a numerical summary of a sample.

   1. Astatistic
   2. Bparameter
   3. Cestimation
   4. Dinference
6. 6A ________ is a numerical summary of a population.

   1. Astatistic
   2. Bparameter
   3. Cestimation
   4. Dinference
7. 7[blank_start]Statistical inference[blank_end] uses sample data to draw conclusions about the entire population

   1. AStatistical inference
8. 8Select the three tools used to take a statistical inference:

   1. ARandom Samples
   2. BEstimations
   3. CProbability
   4. DSampling Distributions
   5. EParameter
   6. FStatistic
9. 9The sampling distribution of as statistic allows us to use the statistic to estimate the value of an unknown population parameter.

   1. ATrue
   2. BFalse
10. 10How Sampling Distributions are used:
    
    To approximate the sampling distribution of a statistic, we:
    -repeatedly select a [blank_start]large[blank_end] number of [blank_start]random[blank_end] samples, size n, from a given population,
    -calculate the value of the [blank_start]statistic[blank_end] for each sample, and
    -produce a [blank_start]histogram[blank_end] of the results

    1. Alarge
    2. Bsmall
    3. Crandom
    4. Dstatistic
    5. Eparameter
    6. Fhistogram
    7. Gbar graph
    8. Hbox-and-whisker plot

11. 11General Properties of Sampling Distributions:
    1. Sampling Distributions can be created for [blank_start]any statistic[blank_end].
    2. Sampling Distributions can be created from samples which come from [blank_start]either a discrete or a continuous[blank_end] distribution.
    3. Sampling Distribution of a statistic often tends to be centered at [blank_start]the value of the population parameter[blank_end] estimated by the statistic.
    4. The spread of the Sampling Distributions of many statistics tends to get [blank_start]smaller[blank_end] as the sample size n [blank_start]increases[blank_end].
    5. As n increases, Sampling Distributions of many statistics become [blank_start]more & more[blank_end] bell-shaped (more like Normal Distributions)

    1. Aany statistic
    2. Bnormal statistics
    3. Cany parameter
    4. Destimated statistics
    5. Eeither a discrete or a continuous
    6. Fa discrete
    7. Ga continuous
    8. Ha Normal
    9. Ithe value of the population parameter
    10. Jthe value of the population statistic
    11. Kzero
    12. Lthe mean
    13. Msmaller
    14. Nlarger
    15. Omore random
    16. Pincreases
    17. Qdecreases
    18. Rmore & more
    19. Sless & less
12. 12For each new sample taken, the sample mean will [blank_start]change[blank_end]

    1. Achange
13. 13The Sampling Distribution of X̅ is also called the sampling distribution of the population mean

    1. ATrue
    2. BFalse
14. 14The sampling distribution of X̅ is the probability distribution that describes the behavior of X̅ in [blank_start]repeated random samples[blank_end] of size n from a population

    1. Arepeated random samples
15. 15Averages are less variable than individual observations

    1. ATrue
    2. BFalse
16. 16Averages are less Normal than individual observations

    1. ATrue
    2. BFalse
17. 17Ways to write population mean:

    1. Aμ
    2. Bμx
    3. CE(x)
    4. DSD(x)
    5. EX
18. 18The symbol for the Sampling Distribution mean is [blank_start]μ sub X̅[blank_end]

    1. Aμ sub X̅
19. 19Ways to write population standard deviation:

    1. Aσ
    2. Bσx
    3. CSD(x)
    4. Dμ
    5. EE(x)
20. 20The symbol for the Sampling Distribution standard deviation is [blank_start]σ sub X̅[blank_end]

    1. Aσ sub X̅
21. 21To emphasize the fact that it describes a sampling distribution, not a population, σX̅ is also called the [blank_start]standard error of X̅[blank_end]

    1. Astandard error of X̅
22. 22Let X: {sample mean of a random sample of size n from a population which has mean of μ and standard deviation σ}
    
    The mean of X̅ is: μx̄ = [blank_start]μ[blank_end]
    The standard deviation of X̅ is: σx̄ = [blank_start]σ/√n[blank_end]
    
    The above equations hold true [blank_start]regardless[blank_end] of the particular form of the population distributions

    1. Aμ
    2. Bσ/√n
    3. Cregardless
23. 23If X~N (μ, σ), then X̅~N (μx̄ = μ, σx̄ = σ/√n)

    1. ATrue
    2. BFalse
24. 24If the [blank_start]sampling[blank_end] distribution of sample mean X̅ is normal, then the population distribution is [blank_start]normal[blank_end]

    1. Asampling
    2. Bnormal
25. 25If the population distribution is not normal (or unknow), then the sampling distribution of X̅ is [blank_start]approximately normal[blank_end] for [blank_start]large[blank_end] n

    1. Aapproximately normal
    2. Blarge
26. 26sample size 'n' is considered sufficiently large if

    1. An ≥ 20
    2. Bn ≥ 30
    3. Cn > 30
    4. Dn > 20
27. 27The mean of two sampling distributions is the same as the population mean μ, but the [blank_start]standard deviation[blank_end] gets [blank_start]smaller[blank_end] as n increases

    1. Astandard deviation
    2. Bsmaller
28. 28If X~N (μ, σ), then X̅~N (μx̄ = μ, σx̄ = σ/√n)
    Empirical Rule:
    ≈[blank_start]68[blank_end]% of X̅ values fall within μx̄ ± [blank_start]1[blank_end]σx̄
    ≈[blank_start]95[blank_end]% of X̅ values fall within μx̄ ± [blank_start]2[blank_end]σx̄
    ≈[blank_start]99.7[blank_end]% of X̅ values fall within μx̄ ± [blank_start]3[blank_end]σx̄

    1. A68
    2. B1
    3. C95
    4. D2
    5. E99.7
    6. F3
29. 29If the population distribution X is normal, then the sampling distribution X̅ is normal.
    
    This implies that Z = (X̅ - μ) / (σ/√n) follows a [blank_start]N(0,1)[blank_end] distribution

    1. AN(0,1)
30. 30The Central Limit Theorem (CLT) states:
    Let X1, ..., Xn be a random sample from a population with mean μ and standard deviation σ. If the population distribution is [blank_start]NOT normal[blank_end], but n is [blank_start]sufficiently large[blank_end], let
    X̅≈N (μx̄=μ, σx̄=σ/√n)
    and let
    Sn ≈ N (μsn = nμ, σsn = σ√n
    
    where Sn = X1+X2+...+Xn is the sum of the sample observations
    

    1. ANOT normal
    2. Bsufficiently large
31. 31Practical Rules Commonly Used:
    1. For sample sizes n ≥ 30, the sampling distribution of the sample mean can be approximated reasonably well by a [blank_start]normal[blank_end] distribution. The approximation gets better as the sample size n becomes [blank_start]larger[blank_end].
    2. If the original population is itself normally distribution, then the sample mean will be [blank_start]normally[blank_end] distributed for [blank_start]any[blank_end] sample size n.

    1. Alarger
    2. Bnormal
    3. Cnormally
    4. Dany
32. 32In an estimation problem, we want to make an educated guess about the value of some population characteristic or population parameter using a [blank_start]point estimate[blank_end] and a [blank_start]confidence interval estimate[blank_end]

    1. Apoint estimate
    2. Bconfidence interval estimate
33. 33A [blank_start]point estimate[blank_end] is a single value used to approximate an unknown population parameter

    1. Apoint estimate
34. 34Examples of point estimates:

    1. Ausing μ ̂ = X̅
    2. Busing p ̂ = X/n
    3. Cusing μ = σ
    4. Dusing X̅ = σ
35. 35A [blank_start]confidence interval[blank_end] is an interval of values used to estimate the true value of an unknown population parameter.
    
    It is associated with a [blank_start]confidence level[blank_end] (C), which is a measure of reliability of a [blank_start]confidence interval[blank_end].

    1. Aconfidence interval
    2. Bconfidence level
    3. Cconfidence interval

Description

Statistics Quiz on Statistics for Scientists and Engineers Final, created by Madison Skeel on 03/05/2022.

Author

Madison Skeel

Language

English

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