Is there a relationship between ABO blood type and Rh factor in undergraduate students at a university? A study involving a sample of 303 undergraduate students at a certain university revealed the following information about their ABO blood type and Rh factor.
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Rh +ve |
Rh -ve |
| A |
108 |
18 |
| B |
24 |
5 |
| AB |
8 |
2 |
| O |
117 |
21 |
Suppose we wish to explore the possibility of a relationship between ABO blood type and Rh factor by carrying out a chi-square test of independence. If we use R to carry out the calculations, we find:
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Pearson's Chi-squared test
data: blood
X-squared = 0.35453, df = 3, p-value = 0.9495
(Some of the expected counts (not shown) are rather small, and while that can be somewhat problematic for this type of test, ignore that issue for the purposes of this question.)
Which of the following statements are true? There may be more than one correct statement; check all that are true.
Question options:
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a)
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The test statistic in this type of chi-square test cannot be negative.
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b)
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This test yields very strong evidence of an association between ABO blood type and Rh factor.
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c)
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One way of expressing the null hypothesis of the chi-square test is that the true mean of ABO blood type equals the true mean of the Rh factor.
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d)
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The p-value in the output is double the area to the right of 0.35453 under a t distribution with 3 degrees of freedom.
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Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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