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. If σ is known, our hypothesis test is known as a z test and we use the z distribution. The formula for the test statistic depends on whether the population standard deviation (σ) is known or unknown. We can also find a confidence interval for the difference in two population proportions.The first step in hypothesis testing is to calculate the test statistic. Confidence Intervals about the Difference Between Two Proportions Step 6 : Based on these results, there is very strong evidence (certainly enough at the 5% level of significance) to support the researcher's claim. Step 5 : Since the P-value < α, we reject the null hypothesis. Researcher claims that faculty vote at a higher rate) P 1 = p f (faculty) and p 1= p s (students) Let's take the two portions in the order we receive them, so Both sample sizes are clearly less than 5% of their respective populations. If 167 of the faculty and 138 of the students voted in the 2008 Presidential election, is there enough evidence at the 5% level of significance to support the researcher’s claim?įirst, we need to check the conditions. She collects data from 200 college faculty and 200 college students using simple random sampling. Problem: Suppose a researcher believes that college faculty vote at a higher rate than college students. What we'll need to do now is develop some similar theory regarding the distribution of the difference in two sample proportions.
In Section 8.2, we discussed the distribution of one sample proportion. The Difference Between Two Population Proportions The information that follows is a bit heavy, but it shows the theoretical background for testing claims and finding confidence intervals for the difference between two population proportions. This isn't an example of a hypothesis test from Section 10.4, about one proportion, it'd be comparing two proportions, so we need some new background. Since we don't have any information from either population, we would need to take samples from each. For example, suppose we want to determine if college faculty voted at a higher rate than ECC students in the 2008 presidential election.
In Chapter 11, we'll be considering the relationship between two populations - means, proportions and standard deviaions.Ī frequent comparison we want to make between to populations is concerning the proportion of individuals with certain characteristics. In Chapters 9 and 10, we studied inferential statistics (confidence intervals and hypothesis tests) regarding population parameters of a single population - the average rest heart rate of students in a class, the proportion of ECC who voted, etc.