The probability of a Type II Error can be calculated by clicking on the link at the bottom of the page. These can be solved using the Two Population Calculator.
Sometimes we're interest in hypothesis tests about two population means. The calculator on this page does hypothesis tests for one population mean. Confidence intervals can be found using the Confidence Interval Calculator. If the hypothesized value of the population mean is outside of the confidence interval, we can reject the null hypothesis. Hypothesis testing is closely related to the statistical area of confidence intervals. Ideally, we'd like to reject the null hypothesis when the alternative hypothesis is true. A Type II Error is committed if you accept the null hypothesis when the alternative hypothesis is true. Ideally, we'd like to accept the null hypothesis when the null hypothesis is true. A Type I Error is committed if you reject the null hypothesis when the null hypothesis is true. There are two types of errors you can make: Type I Error and Type II Error. When conducting a hypothesis test, there is always a chance that you come to the wrong conclusion. To switch from σ known to σ unknown, click on $\boxed$, reject $H_0$. Furthermore, if the population standard deviation σ is unknown, the sample standard deviation s is used instead. Use of the t distribution relies on the degrees of freedom, which is equal to the sample size minus one. If σ is unknown, our hypothesis test is known as a t test and we use the t distribution. The DF is calculated separately for one sample and two sample t-test. If σ is known, our hypothesis test is known as a z test and we use the z distribution. Two Sample T-Test Formula: df (n 1 + n 2) - 2 Where, df Degree of Freedom n 1 Total Number in Sequence 1 n 2 Total Number in Sequence 2. The formula for the test statistic depends on whether the population standard deviation (σ) is known or unknown. As the degrees-of-freedom increase, a t-distribution becomes narrower, taller, and approaches a standard normal distribution.The first step in hypothesis testing is to calculate the test statistic. A t-distribution is more spread out than a standard normal distribution.Ĭ is incorrect. As the degrees-of-freedom increase, a t-distribution becomes wider and flat.Ī t-distribution is a symmetrical, bell-shaped distribution that looks like a normal distribution and has a mean of zero.Ī is incorrect.A t-distribution is symmetric about zero.A t distribution is less spread out than a standard normal distribution.Which of the following statements regarding a t-distribution is most likely correct? The table below represents one-tailed confidence intervals and various probabilities for a range of degrees of freedom. In such a case, the distribution is considered approximately normal.Ī t-statistic, also called the t-score, is given by: Hence, the critical t-value is tc 2.750 tc 2.750. Hence, for a two-tailed test, we need to find the value on the t-distribution with 30 degrees of freedom that has a probability of 0.01/2 0.005 on the right tail. In the absence of explicit normality of a given distribution, a t-distribution may still be appropriate for use if the sample size is large enough for the central limit theorem to be applied. Solution: First, the number of degrees of freedom is df n - 1 31 - 1 30. The population correlation coefficient.The mean difference between paired (dependent) populations.The differences between two population means.When the distribution involved is either normal or approximately normal.Īpart from being used in the construction of confidence intervals, a t-distribution is used to test the following:.