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Q: Which symbol is a test statistic used to test a hypothesis about a population mean?

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The null hypothesis is that there is no change in the population mean while the alternative hypothesis is that there is a change in the mean. The null hypothesis is stated as Ho:Mu=? in statistics while the alternative hypothesis is stated as Ho:Mu(<,>,≠)? depending on whether you are looking for mu to be greater, less than, or not equal to population mean.

You can calculate a result that is somehow related to the mean, based on the data available. Provided that you can work out its distribution under the null hypothesis against appropriate alternatives, you have a test statistic.

Your question is a bit difficult to understand. I will rephrase: In hypothesis testing, when the sample mean is close to the assumed mean of the population (null hypotheses), what does that tell you? Answer: For a given sample size n and an alpha value, the closer the calculated mean is to the assumed mean of the population, the higher chance that null hypothesis will not be rejected in favor of the alternative hypothesis.

Hypothesis

A test statistic is used to test whether a hypothesis that you have about the underlying distribution of your data is correct or not. The test statistic could be the mean, the variance, the maximum or anything else derived from the observed data. When you know the distribution of the test statistic (under the hypothesis that you want to test) you can find out how probable it was that your test statistic had the value it did have. If this probability is very small, then you reject the hypothesis. The test statistic should be chosen so that under one hypothesis it has one outcome and under the is a summary measure based on the data. It could be the mean, the maximum, the variance or any other statistic. You use a test statistic when you are testing between two hypothesis and the test statistic is one You might think of the test statistic as a single number that summarizes the sample data. Some common test statistics are z-score and t-scores.

It depends on whether the hypothesis concerns the mean or the standard error (or variance) or something else.

N is neither the sample or population mean. The letter N represents the population size while the small case letter n represents sample size. The symbol of sample mean is x̄ ,while the symbol for population mean is µ.

Yes.

It means that the statistic that is being tested by the null hypothesis is not significantly different from zero.

μ is the symbol for the population mean in statistics. fyi and related but not necessary for the above answer: the sample mean is , enunciated by saying "x" bar. hope this helped. Citation : http://en.wikipedia.org/wiki/Arithmetic_mean

F is the test statistic and H0 is the means are equal. A small test statistic such as 1 would mean you would fail to reject the null hypothesis that the means are equal.

The sample standard error.

The null hypothesis could be that the 40 students are a sample from the same (or similar) population.

It is a rare to have an unknown population mean and a known population variance

A statistic is a summary measure of some characteristic of a population. If you were to take repeated samples from the population you would not get the same statistic each time - it would vary. And the set of values you would get is its sampling distribution.

A parameter is a number describing something about a whole population. eg population mean or mode. A statistic is something that describes a sample (eg sample mean)and is used as an estimator for a population parameter. (because samples should represent populations!)

A chi-squared test is any statistical hypothesis test in which the sampling distribution of the test statistic is a chi-squared distribution when the null hypothesis is true.

If repeated samples are taken from a population, then they will not have the same mean each time. The mean itself will have some distribution. This will have the same mean as the population mean and the standard deviation of this statistic is the standard deviation of the mean.

A point estimate of a population parameter is a single value of a statistic. For example, the sample mean x is a point estimate of the population mean μ. Similarly, the sample proportion p is a point estimate of the population proportion P.

The population data may be skewed and thus the mean is not a valid statistic. If mean > median, the data will be skewed to the right. If median > mean, the data is skewed to the left.

You use a z test when you are testing a hypothesis that is using proportions You use a t test when you are testing a hypothesis that is using means

a set of individuals,items or data from which a statistic sample is chosen.

The alpha level is the level decided before inferential statistic tests are run at which the null hypothesis may be rejected. The null hypothesis basically states that there is no difference or that a certain claim is true. For example, somebody may say the mean of a population is 50. If we test a sample and find a sample mean different from 50, we may question if the mean of the population really is people. Based on a normal distribution curve, we find how likely it is that we got the result we did assuming the mean really was 50. The alpha level would be determined before hand. If we set the alpha level at .05 and found our result would only occur in 3% of cases if the mean were really 50, we would reject the null hypothesis (In this example the null hypothesis states that the mean is 50). Depending on how important it is to have accurate data, the alpha level may be higher or lower. If in our example the alpha level was .01, the data would not be significant and we would fail to reject the null hypothesis because 3% is greater than 1%.

From Triola, 2009, it is: "The null hypothesis (dented by H0) is a statement that the value of a population parameter (such as proportion, mean, or standard deviation) is equal to some claimed value.".

Many of the quantitative techniques fall into two broad categories: # Interval estimation # Hypothesis tests Interval Estimates It is common in statistics to estimate a parameter from a sample of data. The value of the parameter using all of the possible data, not just the sample data, is called the population parameter or true value of the parameter. An estimate of the true parameter value is made using the sample data. This is called a point estimate or a sample estimate. For example, the most commonly used measure of location is the mean. The population, or true, mean is the sum of all the members of the given population divided by the number of members in the population. As it is typically impractical to measure every member of the population, a random sample is drawn from the population. The sample mean is calculated by summing the values in the sample and dividing by the number of values in the sample. This sample mean is then used as the point estimate of the population mean. Interval estimates expand on point estimates by incorporating the uncertainty of the point estimate. In the example for the mean above, different samples from the same population will generate different values for the sample mean. An interval estimate quantifies this uncertainty in the sample estimate by computing lower and upper values of an interval which will, with a given level of confidence (i.e., probability), contain the population parameter. Hypothesis Tests Hypothesis tests also address the uncertainty of the sample estimate. However, instead of providing an interval, a hypothesis test attempts to refute a specific claim about a population parameter based on the sample data. For example, the hypothesis might be one of the following: * the population mean is equal to 10 * the population standard deviation is equal to 5 * the means from two populations are equal * the standard deviations from 5 populations are equal To reject a hypothesis is to conclude that it is false. However, to accept a hypothesis does not mean that it is true, only that we do not have evidence to believe otherwise. Thus hypothesis tests are usually stated in terms of both a condition that is doubted (null hypothesis) and a condition that is believed (alternative hypothesis). Website--http://www.itl.nist.gov/div898/handbook/eda/section3/eda35.htmP.s "Just giving info on what you don't know" - ;) Sillypinkjade----