₦airaland Forum

I've posted this statistic question over a week now with no solution from any statistician.

1. In his experiment with peas, Gregor Mendel observed that 315 peas where round and yellow, 108 peas where round and green, 101 peas where wrinkled and yellow and 32 where wrinkled and green. According to Mendel's theory of hereditary, the numbers should be in the proportion; 9:3:3:1 when
Significant level @ 0.01%

2. In 200 tosses of a coin, 115 heads and 85 tails where observed, test the hypothesis that the coin is fair using significant level of 0.05%

Because you posted your assignment questions and you can't find someone to solve it for you. You then think it is right to assume there are no statisticians here. Very smart indeed

Anyways quite early to be solving Math, not a statistician per se but i can try with the 2nd question. Maybe later in the day.

okay....i got the time now.

This is simple chi square test.

Solution.

First state your Null and alternative hypothesis. i.e H0 and H1 ( 0 and 1 are both subscript)

H0 - The coin is fair

H1 the coin is biased

secondly we get our observed and expected values.

Our observed values are already given for each category.

Observed values

Heads 115
Tails 85

Total 200

Now our expected values are not given, so we assumed that each toss is equally distributed between the heads and tail. Therefore we say 200/2 =100 that means that 100 tosses for both heads and tails.

Expected values

heads 100
tails 100


total 200

Next we write down our formula and draw a simple table

check the pic below...

Now that we have gotten our x^2

We then calculate our degree of freedom = n-1
where n refers to the number of categories or group i.e heads and tails.
n= 2

d.f= 2-1 =1

From our chisquare tables x^2

@ 5% level same as 0.05 with d.f as 1 = 3.84

i.e x^2 = 3.84

In conclusion: Since the value of x^2 calculated is greater than that from the tables we reject the null hypotheses and conclude that the coin is biased at a significant level of 0.05


phew!! That's all for that question, quite easy and its an interesting topic too

joywendy:
okay....i got the time now.

This is simple chi square test.

Solution.

First state your Null and alternative hypothesis. i.e H0 and H1 ( 0 and 1 are both subscript)

H0 - The coin is fair

H1 the coin is biased

secondly we get our observed and expected values.

Our observed values are already given for each category.

Observed values

Heads 115
Tails 85

Total 200

Now our expected values are not given, so we assumed that each toss is equally distributed between the heads and tail. Therefore we say 200/2 =100 that means that 100 tosses for both heads and tails.

Expected values

heads 100
tails 100


total 200

Next we write down our formula and draw a simple table

check the pic below...

Now that we have gotten our x^2

We then calculate our degree of freedom = n-1
where n refers to the number if categories or group i.e heads and tails.
n= 2

d.f= 2-1 =1

From our chisquare tables x^2

@ 5% level same as 0.05 with d.f as 1 = 3.84

i.e x^2 = 3.84

In conclusion: Since the value of x^2 calculated is greater than that from the tables we reject the null hypotheses and conclude that the coin is biased at a significant level of 0.05


phew!! That's all for that question, quite easy and its an interesting topic too

Thanks. I only said the Statistians here on Nairaland are not active in the Education section.

You should use the same procedure for the first question too.
observed
315
108
101
32
Expected ; since the expected ratio is 9:3:3:1 it mean the proportion is 9/16, 3/16, 3/16, 1/16 therefore,
Expected
315*(9/16)
108*(3/16)
101*(3/6)
32*(1/6)
and your n=4 here
you should get your result.
What is your hypothesis for this question?.

olupentane:
You should use the same procedure for the first question too.
observed
315
108
101
32
Expected ; since the expected ratio is 9:3:3:1 it mean the proportion is 9/16, 3/16, 3/16, 1/16 therefore,
Expected
315*(9/16)
108*(3/16)
101*(3/6)
32*(1/6)
and your n=4 here
you should get your result.
What is your hypothesis for this question?.

You mean the null and the alternate hypothesis?

Olarewajub:
You mean the null and the alternate hypothesis?

Yes

olupentane:
You should use the same procedure for the first question too.
observed
315
108
101
32
Expected ; since the expected ratio is 9:3:3:1 it mean the proportion is 9/16, 3/16, 3/16, 1/16 therefore,
Expected
315*(9/16)
108*(3/16)
101*(3/6)
32*(1/6)
and your n=4 here
you should get your result.
What is your hypothesis for this question?.

nice but i think you missed it up somewhere, especially with the expected values.

He said the number of the peas should be in proportion to 9:3:3:1.

i.e the total peas which is

315+108 +101+32=556

So proportion of those peas that are round and yellow will be

9/16 *556 = 312.75

on and on like that.
i think this should be the hypothesis

H0 : The theory is true, the numbers are of the stated proportion

H1: The theory is false, the numbers are not of the stated proportion.


i may be wrong though, that's one way i know in stating the hypothesis of this question.

Olarewajub:
Thanks. I only said the Statistians here on Nairaland are not active in the Education section.

Nope you said, and I quote
"it is a pity we don't have active statisticians on nairaland,I've posted this statistic question over a week now with no solution from any statistician."

No where was it stated that you were referring to just education section on nl.

Anyways you are welcome

joywendy:
nice but i think you missed it up somewhere, especially with the expected values.

He said the number of the peas should be in proportion to 9:3:3:1.

i.e the total peas which is

315+108 +101+32=556

So proportion of those peas that are round and yellow will be

9/16 *556 = 312.75

on and on like that.
i think this should be the hypothesis

H0 : The theory is true, the numbers are of the stated proportion

H1: The theory is false, the numbers are not of the stated proportion.


i may be wrong though, that's one way i know in stating the hypothesis of this question.

yea you are right. I just want to confirm if he knows what the hypothesis should be. You really know your maths. well done.