In the following problem, check that it is appropriate to use t... | Filo (2024)

FAQs

Is the power of a study 1 minus the probability of committing Type 2 error? ›

The power of a hypothesis test is nothing more than 1 minus the probability of a Type II error. Basically the power of a test is the probability that we make the right decision when the null is not correct (i.e. we correctly reject it).

According to the central limit theorem, the mean of a sample of data will be closer to the mean of the overall population in question, as the sample size increases, notwithstanding the actual distribution of the data. In other words, the data is accurate whether the distribution is normal or aberrant.

The sample size must be greater than or equal to 30 or the population must be normally distributed in order to use the normal model to compute probabilities regarding the sample mean.

Final answer:

The power of a significance test is increased by raising the alpha level, increasing the sample size, and reducing the variability of the data.

What are Type I and Type II errors? In statistics, a Type I error means rejecting the null hypothesis when it's actually true, while a Type II error means failing to reject the null hypothesis when it's actually false.

Pr(Type I error) = Pr(Reject H0| H0 is true)=α. However, in general, the probability of making Type II error, Pr(Type II error) = Pr(Not Reject H0| H0 is false), is different across different test statistics. The power of test is defined as Power = 1-Pr(Type II error) = 1-Pr(Not Reject H0| H0 is false).

The normal distribution assumes that the population standard deviation is known. The t-distribution does not make this assumption. The t-distribution is defined by the degrees of freedom. These are related to the sample size.

The t-distribution, also known as the Student's t-distribution, is a statistical function that creates a probability distribution. The t-distribution is similar to the normal distribution, with its bell shape, but it has heavier tails.

The Central Limit Theorem and Means

In other words, add up the means from all of your samples, find the average and that average will be your actual population mean. Similarly, if you find the average of all of the standard deviations in your sample, you'll find the actual standard deviation for your population.

Normal distribution, also known as the Gaussian distribution, is a probability distribution that appears as a "bell curve" when graphed. The normal distribution describes a symmetrical plot of data around its mean value, where the width of the curve is defined by the standard deviation.

How do you determine if a sample size is normally distributed? ›

Normally Distributed Populations

The Central Limit Theorem says that no matter what the distribution of the population is, as long as the sample is “large,” meaning of size 30 or more, the sample mean is approximately normally distributed.

A normal distribution is a type of continuous probability distribution in which most data points cluster toward the middle of the range, while the rest taper off symmetrically toward either extreme. The middle of the range is also known as the mean of the distribution.

A t-test is often used to compare the difference between two means that are based on samples. The samples come from populations. In that context, the test's statistical power is the probability that you will conclude that the two population means are different when they are different.

The power of a test can be increased in a number of ways, for example increasing the sample size, decreasing the standard error, increasing the difference between the sample statistic and the hypothesized parameter, or increasing the alpha level.

The power of a test is usually expressed as β and the probability of making a Type II error is 1 − β. The power of a study is a function of a study's sample size, the size of the effect one wishes to detect, and the significance level (usually expressed as α) used to guard against Type I error.

The probability of committing a type II error is equal to one minus the power of the test, also known as beta.

Power is the complement of the probability of Type II error -- power = 1−β, not α.

The power of a test is the complement of a type II error or correctly rejecting a false null hypothesis. You can increase the power of the test and hence decrease the type II error by increasing the sample size. Similar to confidence intervals, where we can reduce our margin of error when we increase the sample size.