Question

A peony plant with red petals was crossed with another plant having streaky petals. A geneticist states that 75% of the offspring from this cross will have red flowers. To test this claim, 100 seeds from this cross were collected and germinated, and 53 plants had red petals. Use the chi-square goodness-of-fit test to determine whether the sample data confirm the geneticist's prediction. (Use α = 0.01. Use p1 for the probability of having red flowers and p2 for the probability of having streaky petals.)

Answer 1

Answer:

The sample data confirm the geneticist's prediction that 75% of the offspring from this cross will have red flowers.

Step-by-step explanation:

A Chi-square goodness of fit test can be used to test the claim made by the geneticist.

The hypothesis is defined as:

H₀: There is no difference between the observed and expected value,i.e. p₁ < 0.75.

Hₐ: There is a significant difference between the observed and expected value, i.e. p₁ > 0.75.

The test statistic is:

$\chi^{2}=\sum \frac{(O-E)^{2}}{E}$

Consider the tables attached below.

The value of the test statistic is:

$\chi^{2}=\sum \frac{(O-E)^{2}}{E}=25.8133$

The critical value is:

$\chi^{2}_{\alpha, k-1}=\chi^{2}_{0.01, 1}=6.635$

*Use a Chi-square table.

The critical region is:

$\chi^{2}\geq 6.635$

The test statistic value of 25.8133 lies in the critical region.

The null hypothesis is rejected at 1% level of significance.

Conclusion:

As the null hypothesis is rejected it can be concluded that 75% of the offspring from this cross will have red flowers.