When the correlation between x and y is perfect (r = ±1), the two regression lines are related how?
Correct answer C. They coincide
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Statistics MCQs
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When r = 0, how are the two regression lines placed relative to each other?
Correct answer A. Perpendicular to each other
Given r = 0.5, σx = 4 and σy = 8, what is the regression coefficient of y on x?
Correct answer D. 1.0
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For the data x: 1, 2, 3, 4, 5 and y: 2, 4, 5, 4, 5, what is Pearson’s correlation coefficient (to two decimals)?
Correct answer C. 0.77
For x: 1, 2, 3, 4, 5 and y: 2, 4, 5, 4, 5, what is the least-squares regression line of y on x?
Correct answer A. y = 2.2 + 0.6x
With all else fixed, which change reduces the probabilities of both Type I and Type II errors?
Correct answer B. Increasing the sample size
A population has standard deviation 12. What is the standard error of the mean for samples of size 36?
Correct answer C. 2
For H0: μ = 50 against H1: μ ≠ 50, a sample of 36 gives x̄ = 48 with σ = 6. At the 5% level, what is the conclusion?
Correct answer C. Reject H0 since |z| = 2 exceeds 1.96
Which test is used to compare the variances of two normal populations?
Correct answer D. F-test
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If a one-tailed test gives a p-value of 0.02, what would the corresponding two-tailed p-value be for the same symmetric statistic?
Correct answer B. 0.04
In a test of significance, what does the null hypothesis normally assert?
Correct answer D. There is no real difference or effect
A Type I error occurs when a researcher does what?
Correct answer B. Rejects a null hypothesis that is true
Failing to reject a null hypothesis that is actually false is called what?
Correct answer A. Type II error
The level of significance of a test is the probability of committing which error?
Correct answer C. Type I error
The power of a statistical test is given by which expression?
Correct answer A. 1 − β
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For a two-tailed z-test at the 5% level of significance, what are the critical values?
Correct answer A. ±1.96
For a right-tailed z-test at the 5% level of significance, the critical value of z is approximately what?
Correct answer A. 1.645
For a two-tailed z-test at the 1% level of significance, the critical values are approximately what?
Correct answer B. ±2.576
If the alternative hypothesis is H1: μ > 50, what type of test is being carried out?
Correct answer D. Right-tailed test
Which alternative hypothesis leads to a two-tailed test?
Correct answer D. H1: μ ≠ 40