Commuting Times for College Students The mean travel time to...

Commuting Times for College Students The mean travel time to work for Americans is 25.3 minutes. An employment agency wanted to test the mean commuting times for college graduates and those with only some college. Thirty-five college graduates spent a mean time of 40.5 minutes commuting to work with a population variance of 67.24 . Thirty workers who had completed some college had a mean commuting time of 34.8 minutes with a population variance of $39.69 .$ At the 0.05 level of significance, can a difference in means be concluded?

Key Concepts

Hypothesis Testing

Hypothesis testing is a fundamental statistical procedure that involves making an assumption (the null hypothesis) and then using sample data to decide whether to reject that assumption. It provides a formal framework for validating or refuting claims about population parameters.

Significance Level

The significance level, often denoted as alpha (?), is the threshold for making decisions in hypothesis testing. It represents the probability of making a Type I error, which is rejecting a true null hypothesis. A common value is 0.05, indicating a 5% risk of error.

Two-Sample Comparison

Two-sample comparisons involve evaluating whether there is a statistically significant difference between the means of two independent groups. This approach is applicable when the goal is to infer differences between two populations based on independent samples.

Test Statistic and Standard Error

The test statistic quantifies the difference between the observed sample statistic and the hypothesized population parameter in terms of standard error. The standard error measures the variability of the sampling distribution, and in two-sample tests, it incorporates the sample variances and sizes from both groups.

Transcript

00:01 Okay, so we have a problem about commute time for people who graduated college and for some people who only went and attended some college.

00:11 We want to compare if people who went to college or people who graduated college have a different commune time on average than people who only went through some college.

00:23 In order to do that, we're going to use hypotheses testing and the procedure presented at page 491 of your book.

00:30 So let's get started.

00:32 Step one.

00:33 We gather all our data in one place.

00:35 So the number of people who graduated college, number of people sampled is 35, which is greater than 30.

00:44 Great.

00:45 And the number of people who only attended some college who were sampled is 30, which is greater or equal to 30.

00:57 Another good news.

00:59 On average, the sample of graduated college student is 40 .5 minutes.

01:12 And that's for the sample, of course.

01:15 That's for a sample.

01:16 For the people with some college, a sample on average, had a commute time of 34 .8 minutes.

01:25 The variance for people with graduated college was 67 .24 .24.

01:36 24, not 42, 24, 20.

01:43 Here we go.

01:45 And the various for people with only some college is 39 .69.

01:55 We have all of our data.

01:57 What do we need to do to complete step one is to write down her hypothesis.

02:02 So the no hypothesis, we're going to say that for the population, full population have an equal commute time.

02:09 So people who graduated and some college have the same commute time.

02:13 And for her alternative hypotheses, we're going to say that they have different commute times.

02:19 People who graduated college and people who attended some college have different commute time.

02:25 What does that mean is that we have a two -tail test.

02:31 What we're looking for now in step two will be the critical value that we'll define.

02:37 Our rejection area which is in red...

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