[Warfare]

In hypothesis testing, when they ask to do a TWO-tailed test but not to find out the critical values, how do we do this?
I.e Ho: p = 0.20 Ho : p cannot = 0.20
9 out of 20 read the comics. Test for the change in evidence at 5 % significance..

[raheem94]

(Original post by Warfare)
In hypothesis testing, when they ask to do a TWO-tailed test but not to find out the critical values, how do we do this?
I.e Ho: p = 0.20 Ho : p cannot = 0.20
9 out of 20 read the comics. Test for the change in evidence at 5 % significance..

The significance level will be at each tail, due to the test being two tailed.



Now find this value, it will be less than the significance level, hence we will reject the null hypothesis.

[Warfare]

Okay, but why is it P(X>9)?? When will it be P(X<9) or something. Can you gave me the basic lecture? This is a major issue with the exam coming up and can't get my head wrapped around it?

[raheem94]

(Original post by Warfare)
Okay, but why is it P(X>9)?? When will it be P(X<9) or something. Can you gave me the basic lecture? This is a major issue with the exam coming up and can't get my head wrapped around it?

Stats is not my strongest module, so i am the best person to explain it.

Though i will give it a go,


So there is not point considering this, this won't make the null hypothesis rejected. Looking at the data it is likely that will make the null hypothesis rejected, so my first approach will be to consider this.

[Warfare]

Even if its not your best,I'd say your pretty good at it and you gave me a base to work on. Thanks mate, help is very appreciated!

[raheem94]

(Original post by Warfare)
Even if its not your best,I'd say your pretty good at it and you gave me a base to work on. Thanks mate, help is very appreciated!

I like mechanics and pure, i hate stats!

Do you like it?

[Warfare]

I think stats are easy if you get it, but yeah i agree, i dont like stats at all. Its boring to practice! I enjoy the other modules more

[raheem94]

(Original post by Warfare)
I think stats are easy if you get it, but yeah i agree, i dont like stats at all. Its boring to practice! I enjoy the other modules more

Which modules are you doing?
Are you studying maths or further maths?

[master_blaster66]

is there not alot of peopl;e doing this?

[Warfare]

Im also doing S1,C3,C4,M1,M2 and FP1. What about you?

[raheem94]

(Original post by Warfare)
Im also doing S1,C3,C4,M1,M2 and FP1. What about you?

You can see my TSR profile, to get more information about the modules i am doing or have done.

[Warfare]

Solving Jan 2012 Edexcel S2, I encountered a few problems. Luckily, i had no problems with hypo and hopefully won't anymore. However, i encountered a problem simplifying k^2-k-1 = (1-root5)=2
I might be missing something stupid, but could someone help on that.

The time in minutes that Elaine takes to checkout at her local supermarket follows a
continuous uniform distribution defined over the interval [3, 9].

Given that Elaine has already spent 4 minutes at the checkout,
(d) find the probability that she will take a total of less than 6 minutes to checkout.

I seem to be getting stuck at these type of sums, I've seen the answer, but I need to know how it's coming.

[Anonymous12345]

(Original post by Warfare)
Im also doing S1,C3,C4,M1,M2 and FP1. What about you?

doing c4,c3,fp2,fp3,s2,s3...cramping all these difficult modules together

[master_blaster66]

its the pdf and cdf questions that mess me up

[knowledgecorruptz]

(Original post by Warfare)
Solving Jan 2012 Edexcel S2, I encountered a few problems. Luckily, i had no problems with hypo and hopefully won't anymore. However, i encountered a problem simplifying k^2-k-1 = (1-root5)=2
I might be missing something stupid, but could someone help on that.

The time in minutes that Elaine takes to checkout at her local supermarket follows a
continuous uniform distribution defined over the interval [3, 9].

Given that Elaine has already spent 4 minutes at the checkout,
(d) find the probability that she will take a total of less than 6 minutes to checkout.

I seem to be getting stuck at these type of sums, I've seen the answer, but I need to know how it's coming.

For the first I suggest you sketch the graph (although you've probably already done that seeing as it was the first part of the q). You then just split the total area into two shapes: a rectangle and a trapezium, which will add up to 1. You know the rectangle is worth 0.5, so the remainder (the trapezium) must equal 0.5.

0.5 x height x (short side + long side) = area of trapezium = 0.5
0.5 x (k - 1) x(0.5 + [k -0.5]) = 0.5
Expand and simplify, and then solve for k.

For the first question, DEFINITELY draw the graph. You'll get a rectangle, of length 6 (9 - 3), and height 1/6. Elaine's already spent 4 minutes, so the remaining rectangle now lies between 4 and 9. If you wanted, you could then sketch a new rectangle of height 1/5 and length 5 (9 - 4). Probability of being less than 6 is, therefore:

6 - 4 = 2
2 x 1/5 = 2/5

Hope that helped it's a lot easier to explain with diagrams.

[Warfare]

(Original post by knowledgecorruptz)
For the first I suggest you sketch the graph (although you've probably already done that seeing as it was the first part of the q). You then just split the total area into two shapes: a rectangle and a trapezium, which will add up to 1. You know the rectangle is worth 0.5, so the remainder (the trapezium) must equal 0.5.

0.5 x height x (short side + long side) = area of trapezium = 0.5
0.5 x (k - 1) x(0.5 + [k -0.5]) = 0.5
Expand and simplify, and then solve for k.

For the first question, DEFINITELY draw the graph. You'll get a rectangle, of length 6 (9 - 3), and height 1/6. Elaine's already spent 4 minutes, so the remaining rectangle now lies between 4 and 9. If you wanted, you could then sketch a new rectangle of height 1/5 and length 5 (9 - 4). Probability of being less than 6 is, therefore:

6 - 4 = 2
2 x 1/5 = 2/5

Hope that helped it's a lot easier to explain with diagrams.

Hey thanks helped alot. I got it. The pdf was a tricky one i'd say, I wouldn't have gotten that. Thanks for the help!! Appreciated

[raheem94]

(Original post by knowledgecorruptz)
For the first I suggest you sketch the graph (although you've probably already done that seeing as it was the first part of the q). You then just split the total area into two shapes: a rectangle and a trapezium, which will add up to 1. You know the rectangle is worth 0.5, so the remainder (the trapezium) must equal 0.5.

0.5 x height x (short side + long side) = area of trapezium = 0.5
0.5 x (k - 1) x(0.5 + [k -0.5]) = 0.5
Expand and simplify, and then solve for k.

For the first question, DEFINITELY draw the graph. You'll get a rectangle, of length 6 (9 - 3), and height 1/6. Elaine's already spent 4 minutes, so the remaining rectangle now lies between 4 and 9. If you wanted, you could then sketch a new rectangle of height 1/5 and length 5 (9 - 4). Probability of being less than 6 is, therefore:

6 - 4 = 2
2 x 1/5 = 2/5

Hope that helped it's a lot easier to explain with diagrams.

Good explanation.
+rep to you.

[Groat]

Adding to raheem's definitions, I've taken the definitions from past papers and bolded the words that you must have to get the marks.

Critical Region: The range of values of the test statistic that would lead you to reject the null hypothesis.
Significance Level: The probability of incorrectly rejecting the null hypothesis.
Sampling Frame: A list of all the members of a population.
Population: Collection of all items.
Statistic: A random variable that is a function of the sample values which contains no unknown parameters.
Sampling Distribution: All possible samples of the statistic and their associated probabilities.
Census: Where every member of the population is investigated.
Sampling Unit: An individual member of the sampling frame.
Sample: A subset of a population.
Hypothesis Test: A mathematical procedure to examine a value of a population parameter proposed by the null hypothesis compared with an alternative hypothesis.

Assumptions for Binomial:
Occurrences are independent.
The probability of each outcome remains constant.
Two distinguishable outcomes.
Fixed number of trials.

Assumptions for Poisson:
Events occur singly.
The rate remains constant.
Events are independent.

Binomial approximated to Poisson:
n is large.
p is small.
Mean is near to the variance.

Binomial approximated to Normal:
n is large.
p is close to 0.5.

Poisson approximated to Normal:
Lambda is large.

A sample instead of a census
Saves time.
Cheaper.
Easier.

A census instead of a sample
Known population.
Easily accessible.
Total accuracy.

Continuity correction
Normal is continuous, whereas poisson and binomial are discrete.

[Warfare]

(Original post by Groat)
Adding to raheem's definitions, I've taken the definitions from past papers and bolded the words that you must have to get the marks.

Critical Region: The range of values of the test statistic that would lead you to reject the null hypothesis.
Significance Level: The probability of incorrectly rejecting the null hypothesis.
Sampling Frame: A list of all the members of a population.
Population: Collection of all items.
Statistic: A random variable that is a function of the sample values which contains no unknown parameters.
Sampling Distribution: All possible samples of the statistic and their associated probabilities.
Census: Where every member of the population is investigated.
Sampling Unit: An individual member of the sampling frame.
Sample: A subset of a population.
Hypothesis Test: A mathematical procedure to examine a value of a population parameter proposed by the null hypothesis compared with an alternative hypothesis.

Assumptions for Binomial:
Occurrences are independent.
The probability of each outcome remains constant.
Two distinguishable outcomes.
Fixed number of trials.

Assumptions for Poisson:
Events occur singly.
The rate remains constant.
Events are independent.

Binomial approximated to Poisson:
n is large.
p is small.
Mean is near to the variance.

Binomial approximated to Normal:
n is large.
p is close to 0.5.

Poisson approximated to Normal:
Lambda is large.

A sample instead of a census
Saves time.
Cheaper.
Easier.

A census instead of a sample
Known population.
Easily accessible.
Total accuracy.

Continuity correction
Normal is continuous, whereas poisson and binomial are discrete.

This was extremely useful. Thank you very much

[kanojyoxx]

(Original post by Groat)
Adding to raheem's definitions, I've taken the definitions from past papers and bolded the words that you must have to get the marks.

Critical Region: The range of values of the test statistic that would lead you to reject the null hypothesis.
Significance Level: The probability of incorrectly rejecting the null hypothesis.
Sampling Frame: A list of all the members of a population.
Population: Collection of all items.
Statistic: A random variable that is a function of the sample values which contains no unknown parameters.
Sampling Distribution: All possible samples of the statistic and their associated probabilities.
Census: Where every member of the population is investigated.
Sampling Unit: An individual member of the sampling frame.
Sample: A subset of a population.
Hypothesis Test: A mathematical procedure to examine a value of a population parameter proposed by the null hypothesis compared with an alternative hypothesis.

Assumptions for Binomial:
Occurrences are independent.
The probability of each outcome remains constant.
Two distinguishable outcomes.
Fixed number of trials.

Assumptions for Poisson:
Events occur singly.
The rate remains constant.
Events are independent.

Binomial approximated to Poisson:
n is large.
p is small.
Mean is near to the variance.

Binomial approximated to Normal:
n is large.
p is close to 0.5.

Poisson approximated to Normal:
Lambda is large.

A sample instead of a census
Saves time.
Cheaper.
Easier.

A census instead of a sample
Known population.
Easily accessible.
Total accuracy.

Continuity correction
Normal is continuous, whereas poisson and binomial are discrete.

Also, for a sample you can test to destruction. An example is testing the lifetime of batteries, if you test all of the batteries using a census, then you would have no batteries left; using a sample means you only test some of the batteries so you will still have some left.