Mathematics, 03.01.2020 04:31 Mathinator

According to the mendelian theory of genetics, a certain garden pea plant should produce either white, pink, or red flowers with respective probabilities 1/4, 1/2, and 1/4. to test this theory, a sample of 564 peas was conducted with the result that 141 produced white, 291 produced pink, and 132 produced red flowers. using the chi-square approximation, what conclusion would be drawn at the 5 percent level of significance?

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Answer from: angelrenee2000

$\chi^2 = \frac{(141-141)^2}{141}+\frac{(291-282)^2}{282}+\frac{(132-141)^2}{141}=0.862$

$p_v = P(\chi^2_{2} 0.861)=0.6502$

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(0.861,2,TRUE)"

Since the p value is higher than the significance level 0.65020.05 we FAIL to reject the null hypothesis at 5% of significance, and we can conclude that we don't have significant differences for the proportions assumed.

Step-by-step explanation:

Previous concepts

A chi-square goodness of fit test "determines if a sample data matches a population".

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".

Solution to the problem

Assume the following dataset:

White = 141, Pink = 291, Red= 132

We need to conduct a chi square test in order to check the following hypothesis:

H0: There is no difference with the proportions assumed $p_{white}=1/4, p_{pink}=1/2, p_{red}=1/4$

H1: There is difference with the proportions assumed $p_{white}=1/4, p_{pink}=1/2, p_{red}=1/4$

The level of significance assumed for this case is $\alpha=0.05$

The statistic to check the hypothesis is given by:

$\chi^2 = \sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}$

The table given represent the observed values, we just need to calculate the expected values with the following formula E_i = p_i *Total

And the calculations are given by:

$E_{White} =\fra{1}{4} * 564=141$

$E_{Pink} =\frac{1}{2} *564=282$

$E_{Red} =\frac{1}{4}*564=141$

And now we can calculate the statistic:

$\chi^2 = \frac{(141-141)^2}{141}+\frac{(291-282)^2}{282}+\frac{(132-141)^2}{141}=0.862$

Now we can calculate the degrees of freedom for the statistic given by:

df=categories-1=3-1=2

And we can calculate the p value given by:

$p_v = P(\chi^2_{2} 0.861)=0.6502$

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(0.861,2,TRUE)"

Answer from: Quest

konichiwa~! my name is zalgo and i am here to answer your anime-related question today. more than likely, kirishima would kill izuku, marry mino and kiss momo. all of this would be my opinion by the way. (and i am also a weeb lol)

i hope this you! : d

stay and stay proud! " - zalgo

(and do you think you can mark me as brainliest? i'd greatly appreciate it! arigato~! )

Answer from: Quest

step-by-step explanation:

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