Refer to the Baseball 2016 data, which report information on...

Refer to the Baseball 2016 data, which report information on the 30 Major League Baseball teams for the 2016 season. a. Conduct a test of hypothesis to determine whether the mean salary of the teams was different from $\$ 100.0$ million. Use the .05 significance level. b. Using a $5 \%$ significance level, conduct a test of hypothesis to determine whether the mean attendance was more than 2,000,000 per team.

Refer to the Baseball 2016 data, which report information on the 30 Major League Baseball teams for the 2016 season.
a. Conduct a test of hypothesis to determine whether the mean salary of the teams was different from $\$ 100.0$ million. Use the .05 significance level.
b. Using a $5 \%$ significance level, conduct a test of hypothesis to determine whether the mean attendance was more than 2,000,000 per team.

Key Concepts

Hypothesis Testing

Hypothesis testing is a statistical procedure that involves making an initial assumption about a population parameter (the null hypothesis) and then using sample data to determine whether there is sufficient evidence to reject that assumption in favor of an alternative hypothesis. It provides a structured framework for decision-making in statistics.

Null and Alternative Hypotheses

These are the foundational statements in hypothesis tests. The null hypothesis proposes that there is no effect or difference (for instance, that the mean equals a specified value), while the alternative hypothesis suggests that there is a significant effect or difference. The direction of the alternative hypothesis (greater than, less than, or not equal to) defines whether the test is one-tailed or two-tailed.

Significance Level

The significance level, often denoted as alpha (?), is the threshold for statistical decision-making. It represents the maximum probability of committing a Type I error, which is rejecting the null hypothesis when it is actually true. Common choices for ? are 0.05 or 0.01.

One-sample t-Test

A one-sample t-test is used to determine whether the sample mean significantly differs from a known or hypothesized population mean when the population standard deviation is unknown. This test is particularly useful in small sample sizes where the central limit theorem may not fully apply.

One-tailed and Two-tailed Tests

The choice between a one-tailed and a two-tailed test depends on the research question. A two-tailed test is applied when deviations in both directions (above or below a specified value) are of interest, whereas a one-tailed test focuses on deviations in a single direction (either greater than or less than the specified value).

Transcript

00:01 All right, so we're looking at a baseball data.

00:04 And we want to test if the mean salary of the teams was different from 100 million using the 0 .05 significance level.

00:13 So this is a t test we're going to use because, or a t statistic we're going to use because because it's a sample, sample of salaries.

00:25 So we have the mean and standard deviations here.

00:28 And we need the critical value.

00:30 And it's a two -tailed test because we're saying is not equal.

00:33 To 100 that's the alternative hypothesis whether the no is that no it equals a hundred money so we need to find our critical value 0 .05 that it's going to be a 0 .025 on our table 0 .025 scroll down to 30 degrees or 29 degrees of freedom excuse me because there's there are 30 teams that's a 0 .02 or 2 .054 that's a critical value what's the positive or negative so is it greater than this positive value or is it less than the negative of it so now we can run our our t statistics so it's the mean minus the assume population mean divided by this square of standard deviation which is divided by the square of the sample size of 30 and we should be good to go there we go so it's 2 .9 so we reject the the null hypothesis and we can say yes, at the 0 .05 significance level, the mean side of the teams is different from 100 million.

01:56 Then we're looking for, again, at the 0 .05 significant level, but we're looking for whether the mean attendance was more than 2 million per team.

02:06 So that's the alternative.

02:08 It means greater than 2 million, whereas the null is less than or equal to 2 million.

02:15 Same, um, significant levels, so we're looking at the same column, but of critical value, sorry, it won't be in the same column...

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