91影视

Predicted value: there is ratio of $3$smooth peas for every $3$wrinkled pea

Observed value: $3$smooth and wrinkled peas

The proportions are equal to the mentioned probabilities by the Mendel is stated by the null hypothesis:

$$\begin{gathered} H_0:p_1=\frac{3}{3+1}=0.75 \\ {p}_2=1-p_1=1-0.75=0.25 \end{gathered}$$

or $H_0:p_1=0.75$

Exactly opposite to the null hypothesis is stated by the alternate hypothesis:

$$\begin{gathered} H_a:atleast{p}_{1}isincorrect \\ {H}_a:p_1鈮�0.75 \end{gathered}$$

Hence, null hypothesis and alternate hypothesis are stated above.

$$\begin{gathered} p_1=0.75 \\ {p}_2=0.25 \\ {O}_1=423 \\ {O}_2=133 \\ 鈭�=0.05 \end{gathered}$$

The sample size two categories$\left(c\right)$is: $n=O_1+O_2=423+139=556$

For the first distribution:

$$\begin{gathered} n=556 \\ {p}_1=0.75 \\ {O}_1=423 \end{gathered}$$

Expected frequency is given by:

$E_1=n{p}_1=556脳0.75=417$

The chi-square subtotal is given by:

$$\begin{gathered} {X^2}_{sub1}=\frac{{(O_1-E_1)}^2}{E_1} \\ =\frac{{(423-417)}^2}{417} \\ =0.0863 \end{gathered}$$

For the second distribution:

$$\begin{gathered} n=556 \\ {p}_2=0.25 \\ {O}_2=133 \end{gathered}$$

Expected frequency is given by:

$$\begin{gathered} E_2=n{p}_2 \\ =556脳0.25 \\ =139 \end{gathered}$$

The chi-square subtotal is given by:

$$\begin{gathered} {X^2}_{sub2}=\frac{{(O_2-E_2)}^2}{E_2} \\ =\frac{{(133-139)}^2}{139} \\ =0.259 \end{gathered}$$

The value of the test-statistics is sum of all chi-square subtotals:

$$\begin{gathered} X^2={X^2}_{sub1}+{X^2}_{sub2} \\ =0.0863+0.259 \\ =0.3453 \end{gathered}$$

Now the degree of the freedom of the experiment is the number of categories decreased by $1$.

$df=c-1=2-1=1$

From the table containing the $X^2$ -value in the row $df=1,theP-value$is:

$P>0.25$

By using the chi-square subtotals, value of the test-statistics is estimated.

From the answer of above part:

$P>0.25$

If the $P-$value is less than or equal to the significance level then the null hypothesis is rejected.

$$\begin{gathered} P>鈭� \\ 0.25>0.05 \end{gathered}$$

And here the $P-$value is greater than the significance level that means fail to reject null hypothesis.

As fail to reject the null hypothesis $H_0$which clearly represents that there are no sufficient evidences are provided to reject the null hypothesis or to reject the claim described by the Mendel.