2. Rice is one of the most widely consumed grain worldwide. As increasing global

Question

2. Rice is one of the most widely consumed grain worldwide. As increasing global temperatures hamper rice production, scientists are searching varieties exhibiting some degree of heat resistance. The HT54 variety of the indica rice, Oryza sativa, was found to tolerate several days of high temperatures to 48 degrees Celsius (118 degrees Fahrenheit) during its growth. Researchers performed a genetic crossing experiment between the heat-resistant HT54 variety and a control variety, HT13, without heat resistance. All seedlings in the first generation survived a heat challenge of 48 degrees Celsius. In the second generation only 548 of the 744 plants survived the heat challenge. This would suggest heat resistance is carried by a single gene with a dominant allele and a recessive allele. Are the findings consistent with a simple dominant-recessive Mendelian gen etic model in which F2 is made up of 75% dominant-trait (heat resistance) and recessive-trait rice plants?

a) Perform this test with a Z method.

b) Perform this test with a GOF method.

Explanation / Answer

Null hypothesis : H0 : p = pmendalian = 0.75

Alternative Hypothesis : Ha : p pmendalian = 0.75

(a) Here p0 as per mendelian genetic method = 0.75

and p =548/744 = 0.7365

so Test statistics = (p- p0)/ sqrt [p(1-p)/n] = ( 0.7365 - 0.75)/ sqrt[ 0.75 * 0.25/744]

=- 0.0135/ 0.01587 = - 0.85

and zcritical (95% CI) = -1 .96

so z < zcritical so we can not reject the null hypothesis and can say the findings are consistant with simple dominant recessive mendelian genetic model.

(b) Goodness of Fit Method

n = 744

O1 = 548 and O2 = 196

E1 = 744 * 0.75 = 558 and E2 = 744 * 0.25 = 186

X2 = (548 - 558)2 / 558 + (196 - 186)2 / 186 = 0.1792 + 0.5376 = 0.7168

and for dF = 1 and significance level 0.05 , X2critical = 3.841

so X2 <  X2critical , so we can not reject the null hypothesis and conclude that findings are consistant with simple dominant recessive mendelian genetic model.

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