wont we use the pooled estimate of the common standard deviation. sp = sqrt((n1-1)s1^2 + (n2-1)s2^2)/n1+n2-2) and then use this sp in the test statistic formula??. Pls revert

A pooled standard deviation is used when we assumed we don't know the population variances, and they are EQUAL. In the video, the population variances are assumed to be unknown and UNEQUAL. I hope this helps.

At 4:09, sal took the probability of absolute(t)>than 2.44. Why did he do that, and in which cases would you take less than?

To answer your second question, in addition to what Muhammed El-Yamani said, you would take less than when you need the one-tailed probability; i.e. when your alternative hypothesis states not `μ1 ≠ μ2` but `μ2 - μ1 > 0`.

isn't the P (T is greater than or equal to 2,44) = 0,024 wrong? It should just be 0,012 right? The sentence Sal described in the P-value only contains one side. If he wanted it to contain both, it would have to be P (T is greater than or equal to 2,44 + T is less than or equal to -2,44), or am I wrong?

The way Sal wrote it was a little misleading. He wrote `P(|T| ≥ 2.44)`, notice the || lines. These lines mean absolute value. Since |T| will always be positive, the statement will be true if T is greater than 2.44 or less than -2.44. So, `P(|T| ≥ 2.44) = P(T ≥ 2.44 + T ≤ -2.44) = 0.24` and `P(T ≥ 2.44) = 0.12`. Hope this helps! (:

I don't have a calculator that can calculate the p-value, what can I do instead?

There are two ways: one, which is the more practical option, would be to use a z-table, which gives you the area under a normal distribution for a given z statistic. (http://users.stat.ufl.edu/~athienit/Tables/Ztable.pdf). Another way, which is more complicated, would be to use the formula for the standard normal curve (see http://mathworld.wolfram.com/NormalDistribution.html). Since a p-value is essentially area under this curve, you would have to take the integral of the standard normal curve with the appropriate bounds.

Here you find the p-value of field A on B, but if you find the p-value of field B on A would it be different and why?

If you switched A and B in the subtraction, you would just get a negative result (similar to how 5 - 3 = 2, but 3 - 5 = -2). Then when you used a t-table or the tcdf() function, you would just have to find the area of the high end of the distribution instead of the area of the low end (or vise versa). You should end up with the same result though. Hope this helped! (:

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AP®︎/College Statistics

Course: AP®︎/College Statistics > Unit 11

Lesson 5: Testing for the difference of two population means

Two-sample t test for difference of means

Name: Two-sample t test for difference of means
Uploaded: 2018-03-30T15:22:08Z
Description: Given data from two samples, we can do a signficance test to compare the sample means with a test statistic and p-value, and determine if there is enough evidence to suggest a difference between the two population means.

AP.STATS:

DAT‑3.G (LO)

DAT‑3.G.1 (EK)

DAT‑3.H (LO)

DAT‑3.H.1 (EK)

DAT‑3.H.2 (EK)

VAR‑7 (EU)

VAR‑7.F (LO)

VAR‑7.F.1 (EK)

VAR‑7.G (LO)

VAR‑7.G.1 (EK)

VAR‑7.I (LO)

VAR‑7.I.1 (EK)

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Given data from two samples, we can do a signficance test to compare the sample means with a test statistic and p-value, and determine if there is enough evidence to suggest a difference between the two population means.

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dhruvgsinha
Posted 3 years ago. Direct link to dhruvgsinha's post “wont we use the pooled es...”
wont we use the pooled estimate of the common standard deviation.
sp = sqrt((n1-1)s1^2 + (n2-1)s2^2)/n1+n2-2)
and then use this sp in the test statistic formula??.

Pls revert
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(6 votes)
Answer
- icysuyb
  Posted 3 years ago. Direct link to icysuyb's post “A pooled standard deviati...”
  A pooled standard deviation is used when we assumed we don't know the population variances, and they are EQUAL. In the video, the population variances are assumed to be unknown and UNEQUAL. I hope this helps.
  Comment on icysuyb's post “A pooled standard deviati...”
  (2 votes)
Bjorn Sverre Flatbro
Posted 4 years ago. Direct link to Bjorn Sverre Flatbro's post “isn't the P (T is greater...”
isn't the P (T is greater than or equal to 2,44) = 0,024 wrong? It should just be 0,012 right? The sentence Sal described in the P-value only contains one side. If he wanted it to contain both, it would have to be P (T is greater than or equal to 2,44 + T is less than or equal to -2,44), or am I wrong?
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(2 votes)
Answer
- Evan
  Posted 3 years ago. Direct link to Evan's post “The way Sal wrote it was ...”
  The way Sal wrote it was a little misleading. He wrote
  P(|T| ≥ 2.44), notice the || lines. These lines mean absolute value. Since |T| will always be positive, the statement will be true if T is greater than 2.44 or less than -2.44.
  
  So, P(|T| ≥ 2.44) = P(T ≥ 2.44 + T ≤ -2.44) = 0.24 and P(T ≥ 2.44) = 0.12.
  
  Hope this helps! (:
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  (5 votes)
yaboiudit
Posted 4 years ago. Direct link to yaboiudit's post “At 4:09, sal took the pro...”
At
4:09
, sal took the probability of absolute(t)>than 2.44. Why did he do that, and in which cases would you take less than?
Button navigates to signup pageComment on yaboiudit's post “At 4:09, sal took the pro...”
(3 votes)
Answer
- BootesVoidPointer
  Posted 3 years ago. Direct link to BootesVoidPointer's post “To answer your second que...”
  To answer your second question, in addition to what Muhammed El-Yamani said, you would take less than when you need the one-tailed probability; i.e. when your alternative hypothesis states not μ1 ≠ μ2 but μ2 - μ1 > 0.
  Button navigates to signup page
  (2 votes)
psubbrayanranganatha
Posted 3 years ago. Direct link to psubbrayanranganatha's post “Why don't we use the stan...”
Why don't we use the standard deviation of combined samples as an estimate of the standard deviation (as we are assuming null hypothesis as true for calculating p-value - as mentioned in hypothesis testing for difference in proportions)?
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(3 votes)
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Helen
Posted 5 years ago. Direct link to Helen's post “I don't have a calculator...”
I don't have a calculator that can calculate the p-value, what can I do instead?
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(2 votes)
Answer
- Yellow Shiƒt»
  Posted 5 years ago. Direct link to Yellow Shiƒt»'s post “There are two ways: one, ...”
  There are two ways: one, which is the more practical option, would be to use a z-table, which gives you the area under a normal distribution for a given z statistic. (http://users.stat.ufl.edu/~athienit/Tables/Ztable.pdf).
  
  Another way, which is more complicated, would be to use the formula for the standard normal curve (see http://mathworld.wolfram.com/NormalDistribution.html). Since a p-value is essentially area under this curve, you would have to take the integral of the standard normal curve with the appropriate bounds.
  Button navigates to signup page
  (2 votes)
Iron Programming
Posted 3 years ago. Direct link to Iron Programming's post “When should we assume equ...”
When should we assume equal standard deviations in a test (due to us assuming the null hypothesis)?

I saw it done in a Hypothesis Test but now I'm slightly confused. :\

Any help?
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(2 votes)
Answer
L0ngle
Posted 3 years ago. Direct link to L0ngle's post “Here you find the p-value...”
Here you find the p-value of field A on B, but if you find the p-value of field B on A would it be different and why?
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(1 vote)
Answer
- Evan
  Posted 3 years ago. Direct link to Evan's post “If you switched A and B i...”
  If you switched A and B in the subtraction, you would just get a negative result (similar to how 5 - 3 = 2, but 3 - 5 = -2). Then when you used a t-table or the tcdf() function, you would just have to find the area of the high end of the distribution instead of the area of the low end (or vise versa). You should end up with the same result though.
  
  Hope this helped! (:
  Button navigates to signup page
  (3 votes)
Vikbellamkonda
Posted 3 years ago. Direct link to Vikbellamkonda's post “When would we divide by n...”
When would we divide by n-1?
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(1 vote)
Answer
Rawan Ali
Posted 4 years ago. Direct link to Rawan Ali's post “PROBLEM: The purpose of t...”
PROBLEM: The purpose of this experiment is to determine if attending the review session for the distance education course, Statistics For The Behavioral Sciences: Psyc 2317, will affect scores.
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Delight Joseph
Posted 5 years ago. Direct link to Delight Joseph's post “p-value is said to be the...”
p-value is said to be the smallest significance to reject H0, yet it is also said to be largest significance level to still reject H0. What is the difference in these circumstances?
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(1 vote)
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Video transcript

- [Instructor] "Kaito grows tomatoes in two separate fields. "When the tomatoes are ready to be picked, "he is curious as to whether the sizes of his tomato plants "differ between the two fields. "He takes a random sample of plants from each field "and measures the heights of the plants. "Here is a summary of the results:" So what I want you to do, is pause this video, and conduct a two sample T test here. And let's assume that all of the conditions for inference are met, the random condition, the normal condition, and the independent condition. And let's assume that we are working with a significance level of 0.05. So pause the video, and conduct the two sample T test here, to see whether there's evidence that the sizes of tomato plants differ between the fields. Alright, now let's work through this together. So like always, let's first construct our null hypothesis. And that's going to be the situation where there is no difference between the mean sizes, so that would be that the mean size in field A is equal to the mean size in field B. Now what about our alternative hypothesis? Well, he wants to see whether the sizes of his tomato plants differ between the two fields. He's not saying whether A is bigger than B, or whether B is bigger than A, and so his alternative hypothesis would be around his suspicion, that the mean of A is not equal to the mean of B, that they differ. And to do this two sample T test now, we assume the null hypothesis. We assume our null hypothesis, and remember we're assuming that all of our conditions for inference are met. And then we wanna calculate a T statistic based on this sample data that we have. And our T statistic is going to be equal to the differences between the sample means, all of that over our estimate of the standard deviation of the sampling distribution of the difference of the sample means. This will be the sample standard deviation from sample A squared, over the sample size from A, plus the sample standard deviation from the B sample squared, over the sample size from B. And let's see, we have all the numbers here to calculate it. This numerator is going to be equal to 1.3 minus 1.6, 1.3 minus 1.6, all of that over the square root of, let's see, the standard deviation, the sample standard deviation from the sample from field A is 0.5. If you square that, you're gonna get 0.25, and then that's going to be over the sample size from field A, over 22, plus 0.3 squared, so that is, 0.3 squared is 0.09, all of that over the sample size from field B, all of that over 24. The numerator is just gonna be -.3, divided by the square root of .25 divided by 22, plus .09 divided by 24, and that gets us -2.44. Approximately -2.44. And so if you think about a T distribution, and we'll use our calculator to figure out this probability, so this is a T distribution right over here, this would be the assumed mean of our T distribution. And so we got a result that is, we got a T statistic of -2.44, so we're right over here, so this is -2.44. And so we wanna say what is the probability from this T distribution of getting something at least this extreme? So it would be this area, and it would also be this area, if we got 2.44 above the mean, it would also be this area. And so what I could do is, I'm gonna use my calculator to figure out this probability right over here, and then I'm just gonna multiply that by two, to get this one as well. So the probability of getting a T value, I guess I could say where its absolute value is greater than or equal to 2.44, is going to be approximately equal to, I'm going to go to second, distribution, I'm going to go to the cumulative distribution function for our T distribution, click that. And since I wanna think about this tail probability here that I'm just gonna multiply by two, the lower bound is a very very very negative number, and you could view that as functionally negative infinity. The upper bound is -2.44. - 2.44. And now what's our degrees of freedom? Well if we take the conservative approach, it'll be the smaller of the two samples minus one. Well the smaller of the two samples is 22, and so 22 minus one is 21. So put 21 in there. Two... 21. And now I can paste, and I get that number right over there, and if I multiply that by two, 'cause this just gives me the probability of getting something lower than that, but I also wanna think about the probability of getting something 2.44 or more above the mean of our T distribution. So times two, is going to be equal to approximately 0.024. So approximately 0.024. And what I wanna do then is compare this to my significance level. And you can see very clearly, this right over here, this is equal to our P value. Our P value in this situation, our P value in this situation is clearly less than our significance level. And because of that, we said hey, assuming the null hypothesis is true, we got something that's a pretty low probability below our threshold, so we are going to reject our null hypothesis, which tells us that there is, so this suggests, this suggests the alternative hypothesis, that there is indeed a difference between the sizes of the tomato plants in the two fields.