Question

Variegated Plants. Arabidopsis is a genus of flowering plants related to cabbage. A variegated mutant of the Arabidopsis has yellow streaks or marks. E. Miura et al. studied the origin of this variegated mutant in the article "The Balance between Protein Synthesis and Degradation in Chloroplasts Determines Leaf Variegation in Arabidopsis yellow variegated Mutants" (The Plant Cell, Vol. 19, No. 4, pp. 1313-1328). In a second-generation cross of variegated plants, 216 were variegated and 84 were normal. Genetics predicts that 75% of crossed variegated plants would be variegated and 25% would be normal. At the 10% significance level, do the data provide sufficient evidence to conclude that the second generation of crossed variegated plants does not follow the genetic predictions?

Short answer

Ans: Here, the P-value is greater than the value level.

That is the value of $P(=0.230)>\alpha (=0.10)$.

Therefore, the null hypothesis is not rejected at the role="math" localid="1652086271777" $10\%$level.

Thus, the data do not provide sufficient evidence to conclude that the second generation of variegated crossed plants does not follow genetic predictions at a $10\%$significance level.

Step-by-step solution

Step 1. Given information.

given,

Arabidopsis is a genus of flowering plants related to cabbage. A variegated mutant of the Arabidopsis has yellow streaks or marks. E. Miura et al. studied the origin of this variegated mutant in the article "The Balance between Protein Synthesis and Degradation in Chloroplasts Determines Leaf Variegation in Arabidopsis yellow variegated Mutants"

Step 2. Check that the data provide sufficient evidence to conclude that the second generation of fallen variegated plants does not follow genetic predictions at a 10% significance level.

The hypotheses are given below:

Null hypothesis:

$H_0:-$ The data do not provide sufficient evidence to conclude that the second generation of different plants does not follow genetic predictions.

Another hypothesis:

$H_1:-$ The data provide sufficient evidence to conclude that the second generation of fallen variegated plants does not follow genetic predictions.

Step 3. Use MINITAB to get test statistics and P-value.

MINITAB process:

Step 1: Select Number> Tables> Chi-Square-Goodness-of-Fit Test (One Variable)

Step 2: In the Visual Counts, enter the column of $"O"$.

Step 3: In the category names, enter the PLANT column

Step 4: Under Test, select the $"P"$ column for specific dimensions.

Step 5: Click OK.

Step 4. MINITAB output:-

According to the output, the value of test statics is $1.44$and the p-value is$0.230$.

Step 5. Conclusion:

Here, the P-value is greater than the value level.

That is the value of $P(=0.230)>\alpha (=0.10)$.

Therefore, the null hypothesis is not rejected at the $10\%$ level.

Thus, the data do not provide sufficient evidence to conclude that the second generation of variegated crossed plants does not follow genetic predictions at a $10\%$ significance level.