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4) Statistical Methods > Final - Multiple Choice Questions > Flashcards

Final - Multiple Choice Questions Flashcards

1
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A
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3
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A researcher is told that if the E. coli concentration in the water exceeds the threshold, a notice has to be sent out to stop water consumption so that no one gets sick. What would be the result of a Type I error?

A
  • Sending a notice when there shouldn’t be
  • Incorrect rejection of a true null hypothesis (the E. coli concentration does not exceed the threshold in reality, but is thought to)
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4
Q

A researcher is told that if the E. coli concentration in the water exceeds the threshold, a notice has to be sent out to stop water consumption so that no one gets sick. What would be the result of a Type II error?

A
  • Not sending a notice when there should be
  • Type II error is incorrectly retaining a false null hypothesis (supposing that the E. coli concentration does not exceed the threshold, but in reality it does)
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5
Q

A researcher is told that if the E. coli concentration in the water exceeds the threshold, a notice has to be sent out to stop water consumption so that no one gets sick. How does increasing B affect the outcome of the population?

A

Increases the risk of people getting sick

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6
Q

How does an increase in B affect the power of the test? How does that affect the risk of a Type II error?

A
  • Decreases the power of the test
  • Increases the risk of a Type II error
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7
Q

A researcher is told that if the E. coli concentration in the water exceeds the threshold, a notice has to be sent out to stop water consumption so that no one gets sick. Does raising or lowering the power of the test reduce the risk of people getting sick?

A

Raising the power of the test

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8
Q

True or False: In the ANOVA for an RCBD with 4 replicates per treatment per block, the main effects of the block factor, Bj (j=1,…,n) are i.i.d. N(uB2, 0).

A

False

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9
Q

True or False: In the ANOVA for an RCBD with 4 replicates per treatment per block, if the treatment-by-block interaction is significant, the sum of squares for a “new error term” must be calculated.

A

False, the “new error term” is only calculated if the interaction is NOT SIGNIFICANT.

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10
Q

True or False: In the ANOVA for an RCBD with 4 replicates per treatment per block, the number of degrees of freedom of the “new error term” is obtained by adding the numbers of degrees of freedom for the interaction and the initial error term.

A

True

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11
Q

True or False: In the ANOVA for an RCBD with 4 replicates per treatment per block, when the ranking of mean values per treatment is the same over all blocks, there is potential for a treatment-by-block interaction.

A

False

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12
Q

True or False: An estimator θˆ of the population parameter θ is said to be unbiased and precise if E(θˆ − θ) = 0 and Var(θˆ ) is small.

A

True

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13
Q

True or False: By definition, the analysis of variance F-test is always one-tailed.

A

True

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14
Q

True or False: When testing H0: p = 0.30 against H1: p < 0.30, H0 is rejected when the observed value of the test statistic zobs is less than –z1-α.

A

True

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15
Q

True or False: In a case with two random samples and one qualitative dichotomous variable, the statistical analysis can be done using a chi-square test of independence or a test of two population proportions.

A

False

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16
Q

True or False: When testing H0: μ = μ0 against H1: μ > μ0, with σ2 known, the null hypothesis cannot be rejected when tobs is smaller than t1-α.

A

True, when σ2 known, use the Z-table

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17
Q

True or False: If a 95% confidence interval for μ is calculated to be [7, 9], with X ∼ N (μ, σ2), then the probability that μ is smaller than 7 is 0.05.

A

False, it is 0.025

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18
Q

True or False: If, on average during a certain period, it rains in Ste-Anne 3 times a week, then the number of times it rains in 3 weeks (X) follows a Poisson distribution with E(X) = Var(X) = 9.

A

True

Var(X) = E(X) = m = (3)(3) = 9

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19
Q

True or False: By only increasing the sample size (n), you also increase the confidence level (γ) of a confidence interval if the values of the lower and upper bounds remain unchanged.

A

False

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20
Q

True or False: If some H0 is rejected against some H1 at α = 0.05, then the same H0 is automatically rejected against the same H1 at α = 0.01.

A

False

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21
Q

True or False: A statistically significant positive linear correlation between X and Y necessarily implies that if you run an experiment in which X is decreasing, then Y should respond by increasing automatically.

A

False

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22
Q

True or False: Using blocks in an RCBD with 1 replicate per treatment per block will reduce the Error SS, relative to a CRD, in the ANOVA decomposition.

A

True

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23
Q

True or False: In a chi-square test of independence for a 4 x 3 contingency table, H0 is rejected at α = 0.05 when the observed value of the test statistic is greater than χ20.95(5).

A

False, it is rejected when the observed value is greater than χ20.95(6).

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24
Q

True or False: When performing a t-test to assess the difference between means using two independent random samples ( H0 : μA = μB ), an effective number of degrees of freedom needs to be calculated if the variances are assumed to be equal.

A

False

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25
Q

True or False: The linear model for an RCBD with more than 1 replicate per treatment per block is: Xij = μ + ai + Bj + εij , where μ is the overall population mean, ai represents the main effect of treatment i, Bj is the main effect of block j, and εij represents the experimental error.

A

False, it is Xijk = μ + ai + Bj + (aB)ij+ εijk

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26
Q

True or False: In a two-tailed test, the width of the acceptance region decreases as α decreases.

A

False, the width of the acception region increases as α decreases.

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27
Q

True or False: In the ANOVA for an RCBD with 4 replicates per treatment per block, when the differences between mean values per treatment is the same over all blocks, there is potential for a treatment-by-block interaction.

A

True

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28
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29
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30
Q

A graduate student is told that if the infection index of his plants exceeds the acceptable level, the field must be treated. What would be the result of a Type I error?

A
  • Results in uneccessary treatment of the field
  • Incorrect rejectment of a true null hypothesis (infection index is below the acceptable level in reality)
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31
Q

A graduate student is told that if the infection index of his plants exceeds the acceptable level, the field must be treated. What would be the result of a Type II error?

A
  • Results in not treating the field when it should be
  • Incorrectly retaining a false null hypothesis (the infection index is thought to be below the acceptable level, when it isn’t)
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32
Q

True or False: Increasing B will lower the power of the test.

A

True

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33
Q

A graduate student is told that if the infection index of his plants exceeds the acceptable level, the field must be treated. What would be the result of an increase in the power of the test on the student?

A

Increase the risk that the student will have to start over

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34
Q

True or False: When testing H0: μ = μ0 against H1: μ > μ0, with σ2 known, the decision rule is to reject the null hypothesis at level α when tobs is smaller than t1-α.

A

False, use the Z-table when σ2 is known.

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35
Q

True or False: A Type II error is made when H0 is erroneously accepted, whereas the power of the test is the probability of accepting a true null hypothesis.

A

False, the power of the test is defined as the probability that it will reject a false null hypothesis.

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36
Q

True or False: When testing H0: ρ = 0 against H1: ρ ≠ 0, H0 is rejected at level α when the observed value of the test statistic zobs is less than –z1-α/2 or greater than z1-α/2.

A

False, use the t-table for a linear correlation.

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37
Q

True or False: In a situation where two random samples are collected for one qualitative dichotomous variable – the two random samples are for two levels of a classification factor (e.g., boys and girls), a chi-square test of homogeneity (equality of two population proportions) can be performed.

A

True

38
Q

True or False: An estimator θˆ of population parameter θ is said to be unbiased and not precise if E( θˆ − θ) = 0 and Var(θˆ ) is small.

A

False, the estimator is precise if Var(θˆ ) is small.

39
Q

True or False: If a 99% confidence interval for μ is calculated to be [10, 14], with X ∼ N(μ, σ2), then the probability that μ is greater than 14 is 0.01.

A

False, it is 0.005.

40
Q

True or False: If, on average in a winter, we observe 2 snowfalls every week, then the number of times it snows in 5 winter weeks (X) follows a Poisson distribution with E(X) = Var(X) = 10.

A

True

41
Q

True or False: The length of a confidence interval will increase if you decrease the sample size (n) when the confidence level (γ) remains unchanged.

A

True

42
Q

True or False: If some H0 is rejected against some H1 at α = 0.05, then the same H0 is automatically rejected against the same H1 at α = 0.01.

A

False

43
Q

True or False: A statistically significant negative linear correlation between X and Y necessarily implies that if you run an experiment in which X is decreasing, then Y should respond by increasing overall.

A

True

44
Q

True or False: In an ANOVA for a RCBD with 1 replicate per treatment per block, the number of degrees of freedom used to calculate the LSD is (nb of blocks – 1)(nb of treatments – 1).

A

True

45
Q

True or False: In a chi-square test of independence for a 4 x 4 contingency table, H0 is rejected at α = 0.05 when the observed value of the test statistic is greater than χ20.95(4).

A

False, H0 is rejected when the observed value is greater than χ20.95(9).

46
Q

True or False: When performing a t-test to assess the difference between means using two independent random samples (H0: μA = μB), an effective number of degrees of freedom needs to be calculated if the variances are assumed to be equal.

A

False

47
Q

True or False: The linear model for a RCBD with 1 replicate per treatment per block is: Xij = μ + ai + Bj + (aiBj) + εij , where μ is the overall population mean, ai represents the main effect of treatment i, Bj is the main effect of block j, aiBj is the effect of the treatment-by-block interaction, and εij represents the experimental error.

A

False, it is Xij = μ + ai + Bj + εij.

48
Q

True or False: In a two-tailed test, the width of the acceptance region increases as α decreases.

A

True

49
Q

True or False: In the case of a simple linear regression, the expected value of Y for a given x can be calculated from the linear regression equation, as E(Y) = a + bx + ε.

A

False

50
Q

True or False: In the case of a simple linear regression, the ratio statistic bˆ/Sbˆ has a “Student” t distribution with n – 2 degrees of freedom.

A

True

51
Q

True or False: In the case of a simple linear regression, the estimate of the intercept must be equal to zero for the fitted linear regression model to be significant.

A

False

52
Q

True or False: In the case of a simple linear regression, the value of the estimated slope is comprised between –1 and 1 inclusively.

A

False

53
Q
A
54
Q
A
55
Q

A researcher is required to detect when the contamination level of his soil is above the threshold level. True or False: Increasing α will increase the probability to detect a real difference between the acceptable concentration and the actual concentration of the heavy metal (Reject H0 when it is false).

A

False

56
Q

A researcher is required to detect when the contamination level of his soil is above the threshold level. True or False: Lowering the power of the test will increase the possibility that decontamination will not be done when it should be.

A

False

57
Q

A researcher is required to detect when the contamination level of his soil is above the threshold level. True or False: Increasing β will lower the possibility that decontamination will not be done when it should be.

A

True

58
Q

A researcher is required to detect when the contamination level of his soil is above the threshold level. True or False: Making a Type I error will cause unnecessary costs of decontamination.

A

False

59
Q

True or False: In the linear model for a RCBD with more than 1 replicate per treatment per block, written as Xijk =μ+ai +Bj+(aiBj)+εijk, Bj is the main effect of block j while aiBj is the effect of the treatment-by-block interaction, and both effects are fixed.

A

False, the block and treatment-by-block are not fixed.

60
Q

True or False: In the linear model for a RCBD with 1 replicate, the main effect of block j (Bj ) and the main effect of treatment i (ai) are fixed.

A

False, the effect of the block is not fixed.

61
Q

True or False: For a given confidence level (γ), the length of the confidence interval for one population mean will decrease if the sample variance is increased while the sample size (n) remains the same.

A

False, the length of confidence would increase.

62
Q

True or False: A Type II error is made when a true H0 is rejected, whereas the power of the test is the probability of rejecting a false H0.

A

False, the statement describes a Type I error.

63
Q

True or False: When testing H0 against H1, H0 will be rejected if the probability found using the probability approach is smaller than α.

A

True

64
Q

True or False: Increasing the sample size and the significance level would lower the power of a statistical test.

A

False, it owuld increase the power of the test.

65
Q

True or False: In a test of homogeneity for a 4 x 4 contingency table, H0 is rejected at α = 0.05 when the observed value of the test statistic is greater than F0.95 (3,3).

A

False, H0 is rejected if the observed value is greater than X20.95(9).

66
Q

True or False:

A

False

67
Q

True or False: When testing H0: μa = μb against H1: μa > μb with known σ2a and σ2b, an effective number of degrees of freedom must always be calculated.

A

False

68
Q

True or False: In a left-hand one-tailed test, the critical value of the test statistic decreases when α decreases

A

True

69
Q

True or False: If 3 bus accidents happen every 3 weeks on average in a given part of the world, then the number of bus accidents in a 9-week period there follows a Poisson distribution (X), with E(X) = Var(X) = 9.

A

True

70
Q

True or False: An estimator θˆ of population parameter θ is said to be biased and imprecise if E( θˆ − θ) and Var ( θˆ) is large.

A

False, the estimator would be unbiased.

71
Q

True or False: If a 95% confidence interval for μ is calculated to be [5, 6.5], with X ∼ N(μ, σ2), then the probability that μ is less than 5 is 0.05.

A

False, it is 0.025

72
Q

True or False: If some H0 is rejected against some H1 at α = 0.01, then the same H0 is automatically rejected against the same H1 at α = 0.001.

A

False

73
Q

True or False: When testing H0: ρ = 0 against H1: ρ ≠ 0, H0 is rejected at level α when the observed value of the test statistic, zobs, is smaller than –z1-α/2 or greater than z1-α/2.

A

False, the t-table is utilized for linear correlation.

74
Q

A researcher wants to know how many lettuces are required to detect that the contamination of a certain bacteria is above the accepted standard. What is the effect of increasing B on the consumers?

A

Increases the risk of consumers buying contaminated lettuce

75
Q

A researcher wants to know how many lettuces are required to detect that the contamination of a certain bacteria is above the accepted standard. What is the effect of increasing a on the consumers?

A

Reduces the risk of consumers buying contaminated lettuce

76
Q

A researcher wants to know how many lettuces are required to detect that the contamination of a certain bacteria is above the accepted standard. If lettuce heads exceed the standards, they cannot be sold at the market. What is the effect of a Type I error on the economy of the market?

A

A Type I error could be very costly for the market (incorrect rejection of the null hypothesis; assuming the lettuce heads are contaminated when they are not)

77
Q

A researcher wants to know how many lettuces are required to detect that the contamination of a certain bacteria is above the accepted standard. True or False: increasing the power of the test will reduce the risk of consumers buying contaminated lettuce.

A

True

78
Q

True or False: In the ANOVA for an RCBD with 4 replicates per treatment per block, the mean squares of the new error term is calculated by adding the values of the initial mean squares for the interaction and the error term.

A

False

79
Q

True or False: In the ANOVA for an RCBD with 4 replicates per treatment per block, when the treatment factor is considered fixed, the sum of squares treatment main effects is assumed to be zero under the null hypothesis.

A

True

80
Q

True or False: In the ANOVA for an RCBD with 4 replicates per treatment per block, if the interaction is not significant, a new error term must be calculated.

A

True

81
Q

True or False: In a chi-square test of homogeneity for a 3 x 3 contingency table, H0 is rejected at a=0.05 when the observed value of the test statistic is greater than X20.95(3).

A

False, it is X20.95(4).

82
Q

True or False: in a simple linear regression model, ε denotes the random error, which is assumed to be normally distributed with a population variance of zero.

A

False

83
Q

True or False: when testing H0: p=0.50 against H1: p > 0.50, H0 is rejected at significance level a if the observed value of the test statistic tobs is greater than t1-a(n-1).

A

False

84
Q

True or False: A biased estimator necessarily has a high variance.

A

False

85
Q

True or False: for paired observations (when two observations are collected on the same individual for the same random variable X, (X1, X2) is normally distributed so the difference X1 - X2 = D ~ Bi (uD, o2D).

A
86
Q

True or False: Decreasing the significance level always increases the power of a statistical test.

A

False

87
Q

True or False: A statistically significant negative linear correlation between X and Y implies that when X decreases, Y is expected to respond by decreasing.

A

False

88
Q

True or False: When performing a t-test for the difference between two means in the case of independent random samples (H0: uA = uB), an effective number of degrees of freedom needs to be calculated when a pooled sample variance needs to be used.

A

False

89
Q

True or False: When testing H0: u = u0 against H1: u > u0 with a known population variance, one cannot reject the null hypothesis when Zobs is less than -Z1-a.

A

True

90
Q

True or False: In the estimation of a 95% confidence interval, increasing the sample size will result in a narrower interval.

A

True

91
Q

True or False: A Type II error is made when a false H0 is accepted, whereas the power of the test is the probability of accepting a true H0.

A

False, the power of the test is the probability that it will reject a false null hypothesis.

4) Statistical Methods (12 decks)

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