The appropriate procedure here is a hypothesis test for a single proportion. Hypothesis Testing for the Difference of Two Independent Means, If our confidence interval contains the value claimed by the null hypothesis, then our sample result is close enough to the claimed value, and we therefore do not reject, If our confidence interval does not contain the value claimed by the null hypothesis, then our sample result is different enough from the claimed value, and we therefore reject. When you make an estimate in statistics, whether it is a summary statistic or a test statistic, there is always uncertainty around that estimate because the number is based on a sample of the population you are studying. A Hypothesis Test Regarding Two Population Proportions, 6. A Confidence Interval for the Difference of Two Independent Means, 11. The response variable is full-time employment status which is categorical with two levels: yes/no. A Hypothesis Test for a Population Proportion, 4. The simulation methods used to construct bootstrap distributions and randomization distributions are similar. The confidence interval does not assume this. We should expect to have a p value less than 0.05 and to reject the null hypothesis. The appropriate procedure is a confidence interval for the difference in two means. There are two groups: males and females. The response variable is height, which is quantitative. The real difference is that when you create a confidence interval in conjunction with a hypothesis test, the software ensures that they’re using consistent methodology. A confidence interval is a range of values that is likely to contain an unknown population parameter. Research question: On average, are STAT 200 students younger than STAT 500 students? If you draw a random sample many times, a certain percentage of the confidence intervals will contain the population mean. There are two variables of interest: (1) height in inches and (2) weight in pounds. If we are given a specific population parameter (i.e., hypothesized value), and want to determine the likelihood that a population with that parameter would produce a sample as different as our sample, we use a hypothesis test. Sampling Distribution of the Sample Mean, Section 8: A Confidence Interval for a Population Proportion, 1. We have two independent groups: STAT 200 students and STAT 500 students. There are two variables here: (1) temperature in Fahrenheit and (2) cups of coffee sold in a day. \(p \leq 0.05\), reject the null hypothesis. There is evidence that the population mean is different from 98.6 degrees. Below are a few examples of selecting the appropriate procedure. Cheese consumption, in pounds, is a quantitative variable. The reason for this is that our null hypothesis assumes that p 1 - p 2 = 0. All of the confidence intervals we constructed in this course were two-tailed. The parameter of interest is the correlation between these two variables. A Confidence Interval for Population Mean Difference of Matched-Pairs Data, 8. We are comparing them in terms of average (i.e., mean) age. We have one group: registered voters. Hypothesis tests use data from a sample to test a specified hypothesis. Inference Methods for Dependent Samples, 7. Using Confidence Intervals to Test Hypotheses, 2. The appropriate procedure is a hypothesis test for a single mean. Both variables are quantitative. In other words, if the the 95% confidence interval contains the hypothesized parameter, then a hypothesis test at the 0.05 \(\alpha\) level will almost always fail to reject the null hypothesis. If STAT 200 students are younger than STAT 500 students, that translates to \(\mu_{200}<\mu_{500}\) which is an alternative hypothesis. Because 98.6 is not contained within the 95% confidence interval, it is not a reasonable estimate of the population mean. The variable of interest is age in years, which is quantitative. A Confidence Interval for a Population Proportion Intro, Section 9: Introduction to Hypothesis Testing, Section 10: Hypothesis Test – One Population, 1. If the 95% confidence interval does not contain the hypothesize parameter, then a hypothesis test at the 0.05 \(\alpha\) level will almost always reject the null hypothesis. Research question: On average, how much taller are adult male giraffes compared to adult female giraffes? Inference Methods for Two Population Proportions, 3. We are not given a specific parameter to test, instead we are asked to estimate "how much" taller males are than females. There are two independent groups: STAT 500 students and STAT 200 students.
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