Sixty-eight percent of online courses taught at community...

Sixty-eight percent of online courses taught at community colleges nationwide were taught by full-time faculty. To test if $68 \%$ also represents California's percent for full-time faculty teaching the online classes, Long Beach City College (LBCC) in Califomia, was randomly selected for comparison. In the same year, 34 of the 44 online courses LBCC offered were taught by full-time faculty. Conduct a hypothesis test to determine if $68 \%$ represents California. NOTE: For more accurate results, use more California community colleges and this past year's data.

Key Concepts

Hypothesis Testing

Hypothesis testing is a statistical method used to decide whether there is enough evidence in a sample of data to infer that a certain condition is true for the entire population. It involves comparing observed data against a null hypothesis that represents a default position or established claim.

Null Hypothesis and Alternative Hypothesis

The null hypothesis (H0) is a statement asserting that there is no effect or no difference, serving as a baseline statement (for example, that a population proportion equals a specified value), while the alternative hypothesis (Ha) suggests that there is a difference or effect. These hypotheses are the foundation of the decision-making process in hypothesis testing.

Proportion Testing

Proportion testing involves evaluating whether a sample proportion significantly differs from a known or claimed population proportion. This is important when dealing with data that represent percentages or proportions, such as the fraction of a group possessing a certain characteristic.

Z-test for Proportions

A Z-test for proportions is used when the sampling distribution of the sample proportion can be approximated by a normal distribution. It calculates a Z-statistic by comparing the difference between the sample proportion and the hypothesized proportion with the expected standard error, enabling statisticians to decide whether observed differences can be attributed to random chance.

p-value

The p-value measures the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. A small p-value indicates that such an extreme result is unlikely under the null hypothesis, which may lead to its rejection in favor of the alternative hypothesis.

Significance Level

The significance level, often denoted by alpha (?), is the predetermined threshold for rejecting the null hypothesis. It defines the probability of making a Type I error (incorrectly rejecting a true null hypothesis), and typical values include 0.05 or 0.01.

Transcript

00:01 Hello, welcome to the video, and today we're going to be talking about hypothesis tests, and specifically how to determine whether or not our evidence sufficiently supports our claim.

00:12 So in this problem, we're told that nationwide, 68 % of online courses at community colleges are taught by full -time faculty.

00:21 So we can take this claim here and make it a null hypothesis by saying that we're just going to call this test.

00:31 In this test, we're just going to call this x.

00:33 The proportion of class is taught by full -time faculty.

00:37 It's claimed that x is equal to 0 .68.

00:42 So this is what is claimed to be true for nationwide, all states.

00:49 And the state of california does not believe that this is accurate for their state.

00:57 So they would like to test this alternative hypothesis that x does not equals 0 .68.

01:05 So if we want to visualize this, let's say we have a distribution here with a peak value at the proposed x equals 0 .68.

01:19 With this hypothesis test, we'd like to find evidence to show that the true value of x for the state of california is actually somewhere down here or it could be somewhere up here but the important part is that we'd like to find evidence to show that it is not near 0 .68 and we will be testing this these hypotheses at a 5 % alpha level so to test the hypotheses we do a little survey of our own and we we conduct a survey at long beach city college in california and we find that 34...

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