What is the form of the null hypothesis for a test of a single population mean?
916935
the null hypothesis takes the value of the sample mean while the H1 takes either greater or less the sample mean(1 tailed test)\nu can alaso take the unbiased estimate depending on thequest
324717
what type of statistics?
775942
a hypothesis is an educated guess\nit has to be written as an if, then statement\n For example: If this statement helps you, then i mite get 10 points for the best answer!\ngood luck!
173519
I guess you are talking about the statistical significance, of the difference of two random variables (or functions of variables).\nThat would be the case, for example if you want to test whethern two means are or not equal.\nThen, the difference of the two means can be tested to be or not zero. For that, you need to know the distribution of the original variables.\nIf the two samples come from the same normal population and are of the same size, then the difference is normal with mean zero and variance = 2*sigma^2/n where n is the sample size.\nThen, if the value (In absolute terms) is greater than X(p) then they are significantly different with probability p.\nX(p) is such P(X>X(p))=1-p.
878741
There are certain steps to perform a hypothesis test.\n\n1. Construct a null hypothesis Ho .\n2. Construct a alternate hypothesis H1.\n3. Decide test statistics and parameters [this includes degrees of freedom, significance value] [inmost cases its denoted by Z or t].\n4. Compute the p-value.\n5. Check with the available table.\n6. make inferences wether the hypothesis is accepted or not.\n\nThere is no fixed fomulae for this, but the choice of null hypothesis and test statistics depends on the problem. \n\nThe type of null hypothesis depends on the probelm(wether certain parameters are given or certain distributions are followed by given data etc) and the test statistics depends on parameters.\n\nI hope now you know it.\n\nAll the best
896151
To answer your question, i need to give u an example.\nConsider all real integers from 1 to 10. Let this be our population. \nNow i draw a sample, let this sample be x\nx ={ 3, 4, 5, 6}\nto find population mean, divide the sum of (all integers from 1 to 10) by 10. This will give you 5.4\nnow our population mean is = 5.4\nConsider the sample x now.\nexpectation is the mean of a sample.\nE(X) = (3 + 4 + 5 + 6)/4 = 4.5\nNow, if you take a larger sample (y)\ny = { 2, 3, 4, 5, 6, 7, 8, 9}\nE(Y) = (2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)/8 = 5.5\ncompare this with the population mean, which is 5.4.\nTherefore, if you take a sample of N distinct numbers, where N <10,\n"the expectation of the sample will converge to the population mean as N approaches 10." - this is how the population mean and the expectation of a sample are related.
387360
The problem is incompletely or improperly described.\n\nEach member of the population has some characteristic value.  The mean is the average of this value taken over the entire population, which, assuming each member is an equal contributor, is M = sum(values)/N, where N is the population.  If each member has the same value, say 515, then mean would be 515 and the standard deviation would be zero.  If each even-numbered member has value 1030, and each odd-number member has value 0, the mean is 515 and the standard deviation is (approximately) 515.\n\nSo, you have provided enough information to solve the problem satisfactorily.
43798
I'm assuming this is related to Prob/Stat.\n\nLevel of significance, is simply the accuracy at which you want to perform your tests at. \n\nType 1 & 2 are different kinds of errors associated with Probability. Type 1, if I remember correctly, is if you say the null hypothesis is true, when it is in fact not. A Type 2 error, is saying the null hypothesis is incorrect, when it is in fact correct.
316964
For n = 5? Seriously?\n\nIt is not clear what you are asking.\n\nSuppose that:\n\n1. Your model is of a sequence of independent Bernoulli trials each of which succeeds with probability p.\n\n2. Your null hypothesis H0 is p = 0.3\n\n3. Your alternative hypothesis H1 is p is not 0.3.\n\n4. You plan to observe 5 trials with the intent of accepting or rejecting the null hypothesis with 95% confidence.\n\nThen from p + q = 1 (i.e., q = 1 - p) and 1^5 = (p+q)^5 = p^5 + 5p^4q + 10p^3q^2 + 10p^2q^3 + 5pq^4 + q^5 you know that the probabilities are\n\n5 successes in 5 trials: p^5 = 0.3^5 = 0.00243\n4 succeses in 5 trials: 0.02835\n3 successes: 0.13230\n2 successes: 0.30870\n1 success: 0.36015\n0 successes: 0.16807\n\ni.e., 5 or 4 successes occur <= 5% of the time so you accept H0 on 3 or fewer successes and reject H0 on 4 or 5 successes.\n\nAnother interpretation of your question:\n\nSuppose your model is of independent identical Bernoulli trials each with unknown probability p of success and you would like to estimate p from observing the outcomes of 5 independent trials.  Given k out of 5 successes as the observed outcome for which p can we say that "k" or "k or fewer" or "k or more" successes out of 5 has probability <= 5% of being observed (that is three different questions by the way).  For each of k = 0, 1, ..., 5 you plot the probability of that outcome given p and exclude those p for which the plot drops to 5% or less.
335961
They have to be by definition.  One is the assumed hypothesis (null) and the other is an alternate (what is true if the null hypothesis isn't).  By the very definition of the terms, they can't both be true.  So H0: X= N goes with the alternatve H1: X IS NOT EQUAL to N.
623677
Analysis of variance or ANOVA checks for the variation contributed by teh population in question
488365
Try again Paul C.  The population doesn't need to look normal.\n\nThis all comes down to the Central Limit Theorem.  Let's assume that I take many samples of size 1004 from the population.  Well, each sample will have a percentage that is different from the population percent, because samples are going to look different from the population.  Also, each sample is going to look different from each other, because they are different samples.  If we were to draw a graph that looked at the "behavior" of these many samples, we would notice the following:\n\n1.  If I were to average out all of these sample percents, I would get the population percent.  Hopefully you can see why this would happen.  Sample percents will be around the population percent, but just be off by a little bit.\n\n2.  If I were to look at the spread of the percents, the spread would be smaller as bigger samples were taken.  In other words, if I had taken samples of size 500, the sample percents would be more spread out than for samples of size 1004.  That is because if were take larger samples, then we have more information about the population, so we should expect to get closer to the population percent.\n\n3.  As I take larger and larger samples, the shape of the graph of sample percents would look more and more like a normal curve.  A normal curve is shaped like a bell, where the middle of the bell is were the population percent is.\n\nSo Paul C, it doesn't matter that the population doen't look normal; all we need is a sample that is large enough.\n\nNow the margin of error on polls is typically going to be\n\n2*sqrt(p(1-p)/n))*100%\n\nwhere p is the sample proportion (the sample percent divided by 100%) and n is the sample size.  It can be shown that this margin of error would be at its largest if p = 0.5, so the largest the margin of error would be in this case would be\n\n2*sqrt(0.5*0.5/1004)*100% = 3.2%\n\nThis is typically associated with 95% confidence.  This basically means that if I were again to take many, many samples of size 1004,  95% of the sample percents would be within a margin of error away from the true population percent.\n\nThis of course depends on the sample that is taken.  The online polls that you see would not be good estimates for the population percent.  Below I have a link to a story that MSNBC has on each of its online polls.  The title is "How 1,000 people can be more representative than 200,000."  I think that it is a very good explaination of this topic.
849629
Alpha, as related to level of significance, is purely up to the statistician.  It simply denotes how sure you are of your findings.  The p-value is more descriptive.  The p-value is basically the probability that the statistician will reject the null hypothesis when it in fact should not be rejected.  If the p-value is less than the chosen alpha level, the null hypothesis is rejected.
24979
The simple answer is no.  The K-S (Kolmogorov-Smirnov) test is actually used to test if two data sets have the same distribution, so the previous answer is not correct.  \n\nA T-Test is used when the data comes from an underlying normal population (you can assess that with K-S), and assumes continuous data, and a common unknown variance for both samples.  \n\nWhat exactly are you trying to test?
196477
Root Mean Square is the square root of the sum of the squares. With that terminology is more an electric enginering term, used to measure average powwer.\nFor statistics, its more common to use minimum squares, which refers to the sum of squares of the estimation errors (residuals). Loof for regression on the web.\nGoodness of Fit is a kind of statistical test to prove (or disprove) whether a set of data comes from a given distribution. The most commonly used test for that is the Chi-square test for goodness of fit.\nAbout the third, I don't know.\nHope it Helps.
282565
"z-test" usually refers to normal distribution. Which means \n1) That the population is normal \n2) That the population parameters (mean and variance) are known\nthen you can test against a Z by letting z=(x-mu)/sgima, that distributes normal-standard.\n\nNow, if you don't know the population parameters, then you go the t way (Correctly known as STudent-t to honor its inventor)\n\nNow, t aproaches z as sample size grows. In practical terms, it means that ,for sample sizes below 100 you use t and for larger samples you use normal
713968
The p value is an arbitrary number usually set at .05. It could be anything else, that's just tradition. What you are trying to do is ensure that if a difference in means is noticed, that it is because there is a true difference, not just a difference that can occur by chance. The null hypothesis is saying that there is no difference in means, the alternate hypothesis says there is a difference in means that is greater than chance. That chance is the .05 p value set by you. Therefore, if you're p value is greater than .05, you must accept the null hypothesis, saying that there is greater than a 5% chance that a difference in means is still related to chance alone. Your p value must be less than .05 to reject the null hypothesis.