Question

In fruit flies, purple eyes and ebony body are traits that display autosomal recessive patterns of inheritance. In a
genetics experiment, students cross wild-type flies with flies that have purple eyes and ebony bodies. The students
observe that all the flies in theF1 generation have normal eyes and a normal body color. The students then allow the
F1 flies to mate and produce an F2generation. The students record observations about the flies in the
F2 generation and use the data to perform a chi-square goodness-of-fit test for a model of independent assortment.
The setup for the students' chi-square goodness-of-fit test is presented in Table 1.
Table 1. The students' chi-square goodness-of-fit test for a model of independent assortment
Phenotype
Normal eyes, normal body
Normal eyes, ebony body
Purple eyes, normal body
Purple eyes, ebony body
Observed.
187
49
41
27
Expected
171
57
The students choose a significance level of p=0.01. Which of the following statements best completes the next
step of the chi-square goodness-of-fit test?
a. The calculated chi-square value is 2.11, and the critical value is 7.82.
b. The calculated chi-square value is 2.11, and the critical value is 11.35.
C. The calculated chi-square value is 10.48, and the critical value is 7.82.
d. The calculated chi-square value is 10.48, and the critical value is 11.35.

Answer 1

Answer:

d. The calculated chi-square value is 10.48, and the critical value is 11.35.

Explanation:

The correct option would be option d.

Using the formula for calculating the Chi square ($X^2$):

$X^2 = \frac{(observed frequency - expected frequency)^2}{expected frequency}$

For normal eye, normal body;

$X^2 = \frac{(187 - 171)^2}{171}$ = 1.50

For normal eyes, ebony body;

$X^2 = \frac{(49 - 57)^2}{57}$ = 1.12

For purple eyes, normal body;

$X^2 = \frac{(41 - 57)^2}{57}$ = 4.50

For purple eyes, ebony body;

$X^2 = \frac{(27 - 19)^2}{19}$ = 3.37

Total $X^2$ = 1.50 + 1.12 + 4.50 + 3.37 = 10.48

Degree of freedom = 4 - 1 = 3

Critical value of $X^2$ = 11.35

Hence, the calculated chi-square value is 10.48, and the critical value is 11.35.

The correct option is d.

Answer 2

The Chi-square test is the statistical hypothesis, which is used to calculate the relationship between two categorical variables. It determines the difference between the observed counts and the expected counts.  

The correct answer is:

Option D. The calculated chi-square value is 10.48, and the critical value is 11.35.

The formula for Chi- square test is:

$\text X^2 &=\dfrac{\text{(observed frequency-expected frequency)}^2} {\text {expected frequency}}$

For the normal eyes and normal body, the values are:

$\text X^2&= \dfrac {(187-171)^2}{171}$

X² = 1.50

Now, for normal eyes and ebony body, the values are:

$\text X^2&= \dfrac {(49-57)^2}{57}$

X² = 1.12

Similarly, for purple eyes and normal body, the values are:

$\text X^2&= \dfrac {(41-57)^2}{57}$

X² = 4.50

For purple eyes and ebony body, the values are:

$\text X^2&= \dfrac {(27-19)^2}{19}$

X² = 3.37

Now, the total X² = 1.50 + 1.12 + 4.50 + 3.37 = 10.48

Calculating degree of freedom = 4 - 1 = 3

Therefore, the critical value of  X² can be given as:

Critical value = 11.35

Therefore, Option D is correct.

To know more about the Chi-squared test, refer to the following link:

https://brainly.com/question/15545805