The article "Facebook Use and Academic Performance Among...

The article "Facebook Use and Academic Performance Among College Students," Computers in Human Behavior [2015]: $265-272$ ) estimated that $70 \%$ of students at a large public university in California who are Facebook users log into their Facebook profiles at least six times a day. Suppose that you plan to select a random sample of 400 students at your college. You will ask each student in the sample if they are a Facebook user and if they log into their Facebook profile at least six times a day. You plan to use the resulting data to decide if there is evidence that the proportion for your college is different from the proportion reported in the article for the college in Califomia. What hypotheses should you test? (Hint: See Example $10.3 .)$

The article "Facebook Use and Academic Performance Among College Students," Computers in Human Behavior [2015]:
$265-272$ ) estimated that $70 \%$ of students at a large public university in California who are Facebook users log into their Facebook profiles at least six times a day. Suppose that you plan to select a random sample of 400 students at your college. You will ask each student in the sample if they are a Facebook user and if they log into their Facebook profile at least six times a day. You plan to use the resulting data to decide if there is evidence that the proportion for your college is different from the proportion reported in the article for the college in Califomia. What hypotheses should you test? (Hint: See Example $10.3 .)$

Key Concepts

Sampling Distribution of the Proportion

The sampling distribution of the proportion is the distribution of sample proportions computed from different random samples of a given size from the population. When the sample size is large enough, this distribution can be approximated by a normal distribution, which allows for the use of standard statistical tests to determine how likely it is that the observed sample proportion would occur if the null hypothesis were true.

Hypothesis Testing

Hypothesis testing is a statistical procedure used to assess evidence provided by a sample in making inferences about a population. It involves formulating two competing statements—the null hypothesis and the alternative hypothesis—and using sample data to decide whether there is sufficient evidence to reject the null hypothesis in favor of the alternative.

Null Hypothesis (H0)

The null hypothesis is a statement that asserts there is no effect or no difference between a sample statistic and a specified population parameter. In tests involving proportions, it typically claims that the population proportion equals a certain value, serving as the baseline assumption to be tested against.

Alternative Hypothesis (H1)

The alternative hypothesis is a statement that contradicts the null hypothesis by suggesting that the population parameter differs from the hypothesized value. In the context of a two-tailed test for a proportion, it indicates that the true proportion could be either greater than or less than the specified value.

Two-tailed Test

A two-tailed test is applied when the research hypothesis does not predict the direction of the effect or difference, meaning it tests for the possibility of the parameter being either significantly higher or lower than a specific value. This approach divides the significance level between both extremes of the distribution.

Transcript

0:00 Hello.

00:01 So here our information is that the number of users looked in the poll, that's n, which is 3 ,635.

00:07 The number of users who get news on facebook is going to be x, which is 2 ,472.

00:13 And then the proportion of users who reported getting the news about world events is p not, which is going to be 47%, for 0 .47.

00:20 So then our sample proportion, p -hat, is going to be equal to x over n.

00:26 So that's 2472 divided by 3635, which is going to be approximately equal to 0 .6801.

00:39 And then the standard error is going to be equal to a square root of p .0 times 1 minus p .n over n, giving us 0 .0083.

00:51 And then our hypotheses, we have our alternative hypothesis, h -0, is that p is going to be equal to 0 .47, and then the alternative hypothesis is that p is not equal to 0 .47.

01:07 So then we get our test statistic, z is going to be equal to p hat minus p not over the standard error.

01:16 So that's going to give us approximately 25 .31.

01:20 And the p value is going to be equal to two times the probability that z is going to be greater than 25 .31.

01:38 That's basically just 2 times 0 .0.

01:40 So that's going to be basically 0 .00.

01:43 0.

01:44 So the normal area depicted by the p value can then be illustrated...

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