Difficult# Crossbred Flowers

GMAT-YM6DCG

__Document 1: Data on Crossbred Flowers__

In an experiment, two different species of flowers were crossbred. The resulting 320 flowers were

classified, by color and stigma (the female reproductive part of a flower), into one of four groups, as

shown in the table below.

Flower Type Numbers of Flowers Observed I. Magenta flower with green stigma 170 II. Magenta flower with red stigma 72 III. Red flower with green stigma 47 IV. Red flower with red stigma 31

__Document 2: Description of Chi-Squared Analysis__

The chi-squared statistic is a measurement that indicates how closely a set of observations follows an

expected pattern. In this case, the biologists conducting the crossbreeding research expected a ratio

of 9:3:3:1 for the flower types I:II:III:IV, respectively. The chi-squared computation for a single type of

flower involves taking the difference between the observed number of flowers of that type and the

expected number of flowers of that type (if the biologists had found the exact 9:3:3:1 ratio among the

320 flowers), squaring the difference, and then dividing by the expected number of flowers of that

type. The chi-squared computation is made for each of the four flower types, and the sum of all four

results is found.

__Document 3: Chi-Squared Table__

In the table below, values of chi-squared are given, cross-referenced by the number of degrees of

freedom of the experiment and the tail probability. The number of degrees of freedom (“df”) is one less

than the number of flower types. The smaller tail probabilities (“p”) indicate stronger evidence that the

distribution of flower types does not follow what the biologists expected. The biologists would be

convinced that flower types do not follow the 9:3:3:1 pattern if a tail probability of 0.01 or below

results.

df | .25 | .20 | .15 | .10 | .05 | .025 | .02 | .01 | .005 | .0025 | .001 | .0005 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 1.32 | 1.64 | 2.07 | 2.71 | 3.84 | 5.02 | 5.41 | 6.63 | 7.88 | 9.14 | 10.83 | 12.12 |

2 | 2.77 | 3.22 | 3.79 | 4.61 | 5.99 | 7.38 | 7.82 | 9.21 | 10.60 | 11.98 | 13.82 | 15.20 |

3 | 4.11 | 4.64 | 5.32 | 6.25 | 7.81 | 9.35 | 9.84 | 11.34 | 12.84 | 14.32 | 16.27 | 17.73 |

4 | 5.39 | 5.99 | 6.74 | 7.78 | 9.49 | 11.14 | 11.67 | 13.28 | 14.86 | 16.42 | 18.47 | 20.00 |

5 | 6.63 | 7.29 | 8.12 | 9.24 | 11.07 | 12.83 | 13.39 | 15.09 | 16.75 | 18.39 | 20.51 | 22.11 |

Consider each of the following statements. Does the information in the three sources support the inference as stated?

Yes

No

Yes

No

"There were more flowers of type II observed than the biologists expected."

Yes

No

"The total value of the chi-squared statistic for all four flower types is greater than 10."

Yes

No

"The biologists will be convinced that the flower types do not follow the 9:3:3:1 pattern."