ClickStart over.Introduction:In many experiments, it is not clear immediately if the evidence favors one theoryor another. In these cases, statistical tests can be used to show how probable a given result willbe. In this extension activity, you will learn about a test called thechi-squared test, orχ2test.Question: How can you use a Chi-squared test to test a hypothesis?1.Create a hypothesis: Plant and grow theP1andF1seeds. Open theDevelop hypothesiswindow and fill in all of the possible genotypes for P1, F1, and P2 as you did before.Suppose you started with the hypothesis that the P1 plants wereanl/anl,YGR/YGRand theP2 plants wereANL/ANL,ygr/ygrIf that were true, what would be the genotype of the F1 plants?2.Model: As you did before, throwaway the P1 plants and pollinate theF1 plants. Harvest the resultingseeds into theF2seed bag.Suppose you had the hypothesisthat the F1 plants wereANL/anlYGR/ygr. Fill in the dihybrid Punnettsquare for this cross. If you want,color in the squares to show thecorresponding stem and leaf colors.3.Predict: Suppose you had a total of 16 offspring from this cross. How many of eachphenotype would you expect? Fill in the table with the expected values. Then, predict thenumber of offspring of each phenotype if there were 1,000 offspring, and fill in the secondrow of the table. (Hint: Divide by 16 and multiply by 1,000.).,Number ofoffspringPurple stem,green leafPurple stem,yellow leafGreen stem,green leafGreen stem,yellow leaf161,000Observed4. Grow: ClickReset. Grow the F2 seeds in both containers. Open theclipboardand add theobserved results of your trial to the table above. (Be sureAdd class datais turned off.)(Extension continued on next page)

2019Extension (continued from previous page)5.Calculate: A chi-squared test poses the question: If a given hypothesis is true, how likely is itthat the difference between the observed and expected results is due to chance? If theprobability is very lowthen the hypothesis can be rejected. If the probability is high it doesn’tmean the hypothesis is correct, just that it hasn’t been proven to be incorrect.To do a chi-squared test, first compare the observed results to the expected results. Foreach phenotype, list the observed value (o) and the expected value (e). Then, find thedeviation, oro–e. Square the deviations, and then divide by the expected values. Fill inthe table below for the “single trial” data.PhenotypePurple stem,green leafPurple stem,yellow leafGreen stem,green leafGreen stem,yellow leafObserved (o)Expected (e)Deviation (d) =o–eDeviation squared (d2)d2/eSum all thed2/evalues to find theχ2value:To find thedegrees of freedom, subtract 1 from the number of possible phenotypes:6.Analyze: The table below shows theχ2values, degrees of freedom, and the probability thatthe difference between the expected value and the observed value was just due to chance,rather than due to a flaw in the hypothesis. First, find the row of the table that corresponds tothe degrees of freedom. Then, read across to find theχ2value closest to the one youcalculated. Then, read up to estimate the probability of a chance occurrence.Degrees offreedomProbability that the deviation is due to chance90%80%70%50%30%20%10%5%1%10.0160.0640.1480.4551.0741.6422.7063.8416.63520.2110.4460.7131.3862.4083.2194.6055.9919.21030.5841.0051.4242.3663.6654.6426.2517.81511.34141.0641.6492.1953.3574.8785.9897.7799.48813.277What is the probability that the difference is due to chance?Based on this test, should the hypothesis be rejected?In general, the hypothesis is rejected if the probability that the deviation is due to chance isless than 5%. The chi-squared test cannot be used to accept a hypothesis, however.7. On your own: Turn onAdd class data. Using this data, repeat the chi-squared test, usingthe predictions you made in question 3. Describe your findings on an attached page.

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Zygosity, Fast Plants laboratory