: a.) What is a statistic, anyway? The values a variable can take along with the

Question

: a.) What is a statistic, anyway? The values a variable can take along with their probabilities. A number that summarizes a sample. It estimates the value of a number summarizing a population. A number that summarizes a population. A person randomly selected from a population. A sample of people from a population. b.) What does a confidence interval tell us? The difference between two parameters. A range of plausible values for the value of a statistic from the next random sample. The probability the next statistic falls in that interval. A range of plausible values for the next individual to fall. A range of plausible values for a population parameter. c.) What is a p-value? The probability that the alternative hypothesis is true, given that we observed this value of the statistic. The probability that we would observe a statistic at least as large as the value in the null hypothesis. The probability that we would observe a statistic this much in favor of the alternative hypothesis, if the null hypothesis were true. The probability that the null hypothesis is true, given that we observed this value of the statistic. d.) What does a p-value tell us (for example, in a drug trial)? The variability in the effect of the drug from one person to the next. The size of the effect of the drug. The probability the drug works. The amount of evidence we have that the drug works.

Explanation / Answer

a) statistic :

A statistic (singular) or sample statistic is a single measure of some attribute of a sample (e.g., its arithmetic mean value). It is calculated by applying a function (statistical algorithm) to the values of the items of the sample, which are known together as a set of data.

More formally, statistical theory defines a statistic as a function of a sample where the function itself is independent of the sample's distribution; that is, the function can be stated before realization of the data. The term statistic is used both for the function and for the value of the function on a given sample.

A statistic is distinct from a statistical parameter, which is not computable because often the population is much too large to examine and measure all its items. However, a statistic, when used to estimate a population parameter, is called an estimator. For instance, the sample mean is a statistic that estimates the population mean, which is a parameter.

When a statistic (a function) is being used for a specific purpose, it may be referred to by a name indicating its purpose: in descriptive statistics, a descriptive statistic is used to describe the data; in estimation theory, an estimator is used to estimate a parameter of the distribution (population); in statistical hypothesis testing, a test statistic is used to test a hypothesis. However, a single statistic can be used for multiple purposes – for example the sample mean can be used to describe a data set, to estimate the population mean, or to test a hypothesis.

b) confidence interval :

A range of plausible values for a population parameter.

Confidence intervals consist of a range of values (interval) that act as good estimates of the unknown population parameter. However, the interval computed from a particular sample does not necessarily include the true value of the parameter. Since the observed data are random samples from the true population, the confidence interval obtained from the data is also random. If a corresponding hypothesis test is performed, the confidence level is the complement of the level of significance

c) P value :

The probability that the null hypothesis is true, given that we observed this value of the statistic.

d) The amount of evidence we have that the drug works

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