an individual, produced 25-offspring with his normal-eyed wife. Of their children, 14 were heterochromatic and 11 were-normal. Calculate the chi-square value for this observation. x² = Identify the statement that best interprets the results of the chi-square analysis. Refer to the chi-square distribution table to identify the statement that best interprets the chi-square results. t is not unusal that a heterozygous man produced 14 out of 25 offspring wi heterochromia. The total number of normal offspring is significantly lower than expected. It is unusual that a man with heterochromia had 14 out of 25 offspring with heterochromia. There is a significant difference between the observed number of offspring with heterochromia and the number of offspring that were expected to have heterochromia.

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Suppose a man is heterozygous for heterochromia, an autosomal dominant disorder which causes two different-colored eyes in
an individual, produced 25-offspring with his normal-eyed wife. Of their children, 14 were heterochromatic and 11
were-normal.
Calculate the chi-square value for this observation.
x² =
Identify the statement that best interprets the results of the chi-square analysis. Refer to the chi-square distribution table to
identify the statement that best interprets the chi-square results.
It is not unusal that a heterozygous man produced 14 out of 25 offspring with heterochromia.
The total number of normal offspring is significantly lower than expected.
It is unusual that a man with heterochromia had 14 out of 25 offspring with heterochromia.
There is a significant difference between the observed number of offspring with heterochromia and the number of
offspring that were expected to have heterochromia.
Transcribed Image Text:Suppose a man is heterozygous for heterochromia, an autosomal dominant disorder which causes two different-colored eyes in an individual, produced 25-offspring with his normal-eyed wife. Of their children, 14 were heterochromatic and 11 were-normal. Calculate the chi-square value for this observation. x² = Identify the statement that best interprets the results of the chi-square analysis. Refer to the chi-square distribution table to identify the statement that best interprets the chi-square results. It is not unusal that a heterozygous man produced 14 out of 25 offspring with heterochromia. The total number of normal offspring is significantly lower than expected. It is unusual that a man with heterochromia had 14 out of 25 offspring with heterochromia. There is a significant difference between the observed number of offspring with heterochromia and the number of offspring that were expected to have heterochromia.
Chi-square critical values table
The chi-square (x²) distribution is often used in hypothesis testing to determine whether the deviation between observed and expected values is due to chance or may be
statistically significant. The x² statistic is calculated using the equation
x² = ((O-E)²/E)
where O represents an observed value and E represents an expected value for an observation category. The summation sign Σ indicates that the quotient (O-E)2/E is calculated
for each category and summed over all the categories.
The p value is the probability that the difference between two sets of values is due to chance. The x² value and the following table are used to determine the range in which
the p value falls. In most scientific disciplines, a p value of 0.05 is chosen as the threshold for statistical significance. The degrees of freedom (df) is generally the number of
categories compared minus one.
Critical values of the x² distribution
p value
df 0.950 0.900 0.750 0.500
0.025 0.010 0.005
0.050
3.841
1
5.024 6.635 7.879
2
5.991
7.378 9.210 10.597
3
6.251
7.815
9.348 11.345 12.838
0.250 0.100
0.004 0.016 0.102 0.455 1.323 2.706
0.103 0.211 0.575 1.386 2.773 4.605
0.352 0.584 1.213 2.366 4.108
4 0.711 1.064 1.923 3.357 5.385 7.779 9.488 11.143 13.277 14.860
5 1.145 1.610 2.675 4.351 6.626 9.236 11.070 12.833 15.086 16.750
6 1.635 2.204 3.455 5.348 7.841 10.645 12.592 14.449 16.812 18.548
7 2.167 2.833 4.255 6.346 9.037 12.017 14.067 16.013 18.475 20.278
2.733 3.490 5.071 7.344 10.219 13.362 15.507 17.535 20.090 21.955
3.325 4.168 5.899 8.343 11.389 14.684 16.919 19.023 21.666 23.589
10 3.940 4.865 6.737 9.342 12.549 15.987 18.307 20.483 23.209 25.188
11 4.575 5.578 7.584 10.341 13.701 17.275 19.675 21.920 24.725 26.757
12 5.226 6.304 8.438 11.340 14.845 18.549 21.026 23.337 26.217 28.300
13 5.892 042 9.299 12.340 15.984 19.812 22.362 24.736 27.688 29.819
14 6.571 7.790 10.165 13.339 17.117 21.064 23.685 26.119 29.141 31.319
15 7.261 8.547 11.037 14.339 18.245 22.307 24.996 27.488 30.578 32.801
20 10.851 12.443 15.452 19.337 23.828 28.412 31.410 34.170 37.566 39.997
50 34.764 37.689 42.942 49.335 56.334 63.167 67.505 71.420 76.154 79.490
100 77.929 82.358 90.133 99.334 109.141 118.498 124.342 129.561 135.807 140.169
89
Transcribed Image Text:Chi-square critical values table The chi-square (x²) distribution is often used in hypothesis testing to determine whether the deviation between observed and expected values is due to chance or may be statistically significant. The x² statistic is calculated using the equation x² = ((O-E)²/E) where O represents an observed value and E represents an expected value for an observation category. The summation sign Σ indicates that the quotient (O-E)2/E is calculated for each category and summed over all the categories. The p value is the probability that the difference between two sets of values is due to chance. The x² value and the following table are used to determine the range in which the p value falls. In most scientific disciplines, a p value of 0.05 is chosen as the threshold for statistical significance. The degrees of freedom (df) is generally the number of categories compared minus one. Critical values of the x² distribution p value df 0.950 0.900 0.750 0.500 0.025 0.010 0.005 0.050 3.841 1 5.024 6.635 7.879 2 5.991 7.378 9.210 10.597 3 6.251 7.815 9.348 11.345 12.838 0.250 0.100 0.004 0.016 0.102 0.455 1.323 2.706 0.103 0.211 0.575 1.386 2.773 4.605 0.352 0.584 1.213 2.366 4.108 4 0.711 1.064 1.923 3.357 5.385 7.779 9.488 11.143 13.277 14.860 5 1.145 1.610 2.675 4.351 6.626 9.236 11.070 12.833 15.086 16.750 6 1.635 2.204 3.455 5.348 7.841 10.645 12.592 14.449 16.812 18.548 7 2.167 2.833 4.255 6.346 9.037 12.017 14.067 16.013 18.475 20.278 2.733 3.490 5.071 7.344 10.219 13.362 15.507 17.535 20.090 21.955 3.325 4.168 5.899 8.343 11.389 14.684 16.919 19.023 21.666 23.589 10 3.940 4.865 6.737 9.342 12.549 15.987 18.307 20.483 23.209 25.188 11 4.575 5.578 7.584 10.341 13.701 17.275 19.675 21.920 24.725 26.757 12 5.226 6.304 8.438 11.340 14.845 18.549 21.026 23.337 26.217 28.300 13 5.892 042 9.299 12.340 15.984 19.812 22.362 24.736 27.688 29.819 14 6.571 7.790 10.165 13.339 17.117 21.064 23.685 26.119 29.141 31.319 15 7.261 8.547 11.037 14.339 18.245 22.307 24.996 27.488 30.578 32.801 20 10.851 12.443 15.452 19.337 23.828 28.412 31.410 34.170 37.566 39.997 50 34.764 37.689 42.942 49.335 56.334 63.167 67.505 71.420 76.154 79.490 100 77.929 82.358 90.133 99.334 109.141 118.498 124.342 129.561 135.807 140.169 89
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