Statistics Marathon & Questions (2 Viewers)

davidgoes4wce · May 28, 2016

Re: University Statistics Discussion Marathon

Speaking of Statistics have any of you guys used R Programming and Statistical software? (for say work or university purposes)?

I want to be more proficient at this software and I enjoy using it in comparison to Excel, SPSS or Minitab for that matter as the speed is alot quicker.

Trebla · May 28, 2016

University Statistics Discussion Marathon

BlueGas said:
Yeah that's the easy part but what's the interpretation of the p value? That's the part which I need to understand. The two figures I posted (the one you helped me in and the second one now) have different null and alternative hypothesis tests.

The p-value is the probability of an observation occurring assuming the null hypothesis is actually true. If the p-value is very low then the observation you see is very unlikely if the null hypothesis is true. If you believe the observation you see is typical (has a higher probability of occurring) then it is likely that your assumption may not be right, hence the decision reject it.

davidgoes4wce said:
Speaking of Statistics have any of you guys used R Programming and Statistical software? (for say work or university purposes)?

I want to be more proficient at this software and I enjoy using it in comparison to Excel, SPSS or Minitab for that matter as the speed is alot quicker.

I've used R once upon a time

davidgoes4wce · May 28, 2016

Re: University Statistics Discussion Marathon

Trebla said:
The p-value is the probability of an observation occurring assuming the null hypothesis is actually true. If the p-value is very low then the observation you see is very unlikely if the null hypothesis is true. If you believe the observation you see is typical (has a higher probability of occurring) then it is likely that your assumption may not be right, hence the decision reject it.

I've used R once upon a time

There seems to be alot of jobs out there for people who are skilled up in R and SPSS. It pays to focus on one or two specific areas.

davidgoes4wce · May 28, 2016

Re: University Statistics Discussion Marathon

Topic of this question is Sum and Difference of independent normal variates

Is there a mistake in this question? I get the feeling that they have substituted the wrong value of 40 in , which should have been 20.
$$ In this question there is an assumption that $ \mu=20 $ and a $ \sigma=4$

davidgoes4wce · May 28, 2016

Re: University Statistics Discussion Marathon

$$ According to a recent poll, 29 \% of adults in a certain area have high levels of cholesterol. They report that such elevated levels could be financially devasting to the regions healthcare system and are a major concern to health insurance providers. According to recent studies, cholesterol levels in healthy adults from the area average about 210 mg/DL, with a standard deviation of 20 mg/DL, and are roughly Normally distributed. If the cholesterol levels of a sample of 47 healthy adults from the region is taken, answers part (a) through (d).$

$(a) MCQ. What shape will the sampling distribution of the mean have?$

$a) The sampling distribution of the mean is skewed right$
$b) The sampling distribution of the mean is skewed left$
$c) The sampling distribution of the mean is normal$
$d) There is not enough information to determine the shape of the sampling distribution$

$(b) What is the mean of the sampling distribution ?$

$(c) What is the standard deviation?$

$(d) If the sampling distribution were increased to 90, how would your answers to parts (a) - (c) change?$

$for part (a), the shape of the distribution would? a = also be normally distributed, b = become skewed left, c = become skewed right$

$- for part (b), the mean of the sampling distribution would? a = change to, b = remain as .... if it is suppose to change, what is the new sampling distribution?$

$-for part (c), the standard deviation of the sampling distribution would? a = change to, b = remain as .... if it is suppose to change, what is the new standard deviation?$

davidgoes4wce · May 29, 2016

Re: University Statistics Discussion Marathon

davidgoes4wce said:
$$ According to a recent poll, 29 \% of adults in a certain area have high levels of cholesterol. They report that such elevated levels could be financially devasting to the regions healthcare system and are a major concern to health insurance providers. According to recent studies, cholesterol levels in healthy adults from the area average about 210 mg/DL, with a standard deviation of 20 mg/DL, and are roughly Normally distributed. If the cholesterol levels of a sample of 47 healthy adults from the region is taken, answers part (a) through (d).$

$(a) MCQ. What shape will the sampling distribution of the mean have?$

$a) The sampling distribution of the mean is skewed right$
$b) The sampling distribution of the mean is skewed left$
$c) The sampling distribution of the mean is normal$
$d) There is not enough information to determine the shape of the sampling distribution$

$(b) What is the mean of the sampling distribution ?$

$(c) What is the standard deviation?$

$(d) If the sampling distribution were increased to 90, how would your answers to parts (a) - (c) change?$

$for part (a), the shape of the distribution would? a = also be normally distributed, b = become skewed left, c = become skewed right$

$- for part (b), the mean of the sampling distribution would? a = change to, b = remain as .... if it is suppose to change, what is the new sampling distribution?$

$-for part (c), the standard deviation of the sampling distribution would? a = change to, b = remain as .... if it is suppose to change, what is the new standard deviation?$

$Here is my attempt at this question$

$(a) Shape will be bell shaped i.e. mean is normal$

$(b) Mean of sampling distribution is 210$

$$ (c) Standard deviation $ = \frac{\sigma}{\sqrt{n}}=\frac{20}{\sqrt{47}}=2.917$

$(d) If we increase the sample size to 90. Then the shape of distribution would be Normally Distributed.$

$Mean will Remain the same$

$$ Standard deviation = $ \frac{20}{\sqrt{90}}=2.108$

$$ Hence it will increase sample size then standard deviation will be decreased.$

davidgoes4wce · May 31, 2016

Re: University Statistics Discussion Marathon

$$ An analyst collected data from 25 randomly selected transactions and found the purchase amounts $ (in \$). $ The mean is $ \$29.92 and the standard deviation is \$14.40. $ The analyst wants to know if the mean purchase amount of all transactions is at least $ \$24. $ What is the P-value of the test statistic $ ?$

$How would you type this code in Excel to determine the P-Value ?$

davidgoes4wce · May 31, 2016

Re: University Statistics Discussion Marathon

I'll admit I got this question from a quiz and from my understanding reading a textbook (which shows Excel cell calculation) my interpretation of this calculation is it should be :

= T.DIST.RT((25.23-19)/14.03, 24)

$$ It's based on the t-test statistic formula $ t=\frac{\bar{x}-\mu}{{s} \div \sqrt{n}}$

$$ Degrees of Freedom in this case $ = 24 \ df$

davidgoes4wce · Jun 1, 2016

Re: University Statistics Discussion Marathon

$$ It is recommended that adults get 8 hours of sleep each night. A researcher hypothesized college students get less than the recommended number of hours of sleep each night, on average. The researcher randomly sampled 20 college students and obtained a p-value of 0.10. Suppose the researcher sampled more college students and that the sample mean and sample standard deviation stayed the same. Would the P-Value be lower, be higher, or stay the same $ ?$

BlueGas · Jun 1, 2016

Re: University Statistics Discussion Marathon

davidgoes4wce said:
$$ It is recommended that adults get 8 hours of sleep each night. A researcher hypothesized college students get less than the recommended number of hours of sleep each night, on average. The researcher randomly sampled 20 college students and obtained a p-value of 0.10. Suppose the researcher sampled more college students and that the sample mean and sample standard deviation stayed the same. Would the P-Value be lower, be higher, or stay the same $ ?$

I'm guessing that the p value would change but I don't know lol, would like to know the answer though.

davidgoes4wce · Jun 1, 2016

Re: University Statistics Discussion Marathon

Me too I've been thinking about it for a few days......................im guessing it would be lower. I read somewhere if you increase the sample size the p-value decreases slightly.

nerdasdasd · Jun 1, 2016

Re: University Statistics Discussion Marathon

davidgoes4wce said:
Me too I've been thinking about it for a few days......................im guessing it would be lower. I read somewhere if you increase the sample size the p-value decreases slightly.

If the mean or SD didn't change, that means the Z score probably didn't change right ?

If that doesn't change, the p value doesn't change too .

davidgoes4wce · Jun 1, 2016

Re: University Statistics Discussion Marathon

nerdasdasd said:
If the mean or SD didn't change, that means the Z score probably didn't change right ?

If that doesn't change, the p value doesn't change too .

OK I'll take your word for it. I'll look to read up on it a bit further as I have actually never thought it about it in too much detail.

seanieg89 · Jun 1, 2016

Re: University Statistics Discussion Marathon

My stats knowledge is minimal, but wouldn't it decrease?

I assume that whats going on is you have the hypothesis that the avg sleeping hours of a student are normally distributed with mean 8 and variance V. We are doing a one-tailed test with test statistic our sample mean.

If our p-value is 0.1 that means the observed sample mean m of our initial sample of 20 students is quite a bit less than 8. (So the probability of a randomly selected student from our population sleeping less than m hours on average is only 0.1).

But the distribution of sample means in samples of size n is given by N(8,V/n). So as n increases, the probability of the the test statistic being smaller than m decreases, i.e. the p-value decreases.

Is there some other choice of hypothesis/test statistic here? Without specifying such a choice, the one I have made above seems natural to me.

davidgoes4wce · Jun 1, 2016

Re: University Statistics Discussion Marathon

seanieg89 said:
My stats knowledge is minimal, but wouldn't it decrease?

I assume that whats going on is you have the hypothesis that the avg sleeping hours of a student are normally distributed with mean 8 and variance V. We are doing a one-tailed test with test statistic our sample mean.

If our p-value is 0.1 that means the observed sample mean m of our initial sample of 20 students is quite a bit less than 8. (So the probability of a randomly selected student from our population sleeping less than m hours on average is only 0.1).

But the distribution of sample means in samples of size n is given by N(8,V/n). So as n increases, the probability of the the test statistic being smaller than m decreases, i.e. the p-value decreases.

Is there some other choice of hypothesis/test statistic here? Without specifying such a choice, the one I have made above seems natural to me.

With these MCQ questions (they were given to UNSW business statistics students)

The section or topic of the quiz , the majority of the questions were based on the t-test.

$t=\frac{\bar{x}-\mu}{s \div \sqrt{n}}$

davidgoes4wce · Jun 1, 2016

Re: University Statistics Discussion Marathon

The more I think about it the more I think the P-Value actually decreases

$I'll provide 2 cases where we are hypothesizing where we make a claim that the students under sleep (lets say 6 hours). I've always like using real numbers, we make an assumption that $ \mu=8 $ and s=2 do not change in both cases.$

Case 1:

$\bar{x}=6, \mu=8, s=2, n =20$

$t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}=\frac{6-8}{2 \div \sqrt{20}}=-4.472$

$The $ t_{stat}=-4.472 $ at 19 degrees of Freedom, gives a P-Value = 0.000131$

Case 2:

$\bar{x}=6, \mu=8, s=2, n=100$

$t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}=\frac{6-8}{2 \div \sqrt{100}}-34.00$

$The $ t_{stat}=-34 $ at 99 degrees of Freedom, gives a P-Value = 1.04 E-56$

So what I can interpret from this is it decreases.

davidgoes4wce · Jun 1, 2016

Re: University Statistics Discussion Marathon

Also I will admit , I did not know how to calculate a P-Value manually up until last week. (having studied high school stats+ uni stats for around 6 years) If you guys are looking to get better at statistics with Excel highly recommend this book by : Mark Berenson, David Levine and Kathryn Szabat, BUSS1020 Quantitative Business Analysis.

I personally feel they explain stats better than the Science, Advanced Science, Engineering or Psychology way of statistics.

seanieg89 · Jun 1, 2016

Re: University Statistics Discussion Marathon

Sure, if you are using the t-test then use that formula instead, it will still decrease. You can compute the p-value in terms of n by using the t-distribution and show it decreases by using calculus or whatever else you like.

Just think about it intuitively, a sample of two students who on average undersleep by H hours is far less significant than a sample of 1,000,000 students who on average undersleep by the same amount. (With both samples having the same s.d.)

The latter is far greater evidence of a trend of undersleeping students, and any reasonable statistical test should reflect this.

davidgoes4wce · Jun 2, 2016

Re: University Statistics Discussion Marathon

$Consider a sample size n=10 where the first sample mean is 8 and sample variance is 13. Consider a second sample that is exactly the same as the first excerpt that there is an additional observation that takes on the value of 8. What is the sample variance for this larger sample with n=11 observations? (Your answer should be correct to 1 decimal place.)$

Ans : 11.7

davidgoes4wce · Jun 2, 2016

Re: University Statistics Discussion Marathon

This is the theory behind the above question

It seems like in that 2nd line of working, they did an expansion, I for one could not see that expansion of

$\sum(y_{i}-\bar{y})^2=\sum \ y_{i} ^2 -2 \bar{y} \sum \ y_i + n \bar{y}^2$

$Would it be ok to write that summation ?$

$\sum(y_{i}-\bar{y})^2=\sum \ y_{i} ^2 -2 \sum \bar{y} \ y_i + n \bar{y}^2$

I got a bit lost with the 'n' chucked in the third term of the expansion as well.

Statistics Marathon & Questions (2 Viewers)

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