Testing the Difference Between Two Means (f) interpret the decision in the context of the original claim. Assume the samples are random and dependent, and the populations are normally distributed.
[APPLET] Passing Play Percentages The passing play percentages of 10 randomly selected NCAA Division 1A college football teams for home and away games in the 2020–2021 season are shown in the table. At , α=0.20 is there enough evidence to support the claim that passing play percentage is different for home and away games? (Source: TeamRankings)

Verified step by step guidance

1. Step 1: Identify the problem as a paired-sample t-test since the data involves dependent samples (home and away passing play percentages for the same teams). The goal is to test if there is a significant difference between the means of the two conditions.
2. Step 2: State the null hypothesis (H₀) and the alternative hypothesis (H₁). H₀: The mean difference in passing play percentages between home and away games is 0 (μd = 0). H₁: The mean difference in passing play percentages between home and away games is not 0 (μd ≠ 0).
3. Step 3: Calculate the differences (d) between the home and away passing play percentages for each team. Then, compute the mean of these differences (d̄) and the standard deviation of the differences (s_d).
4. Step 4: Use the formula for the test statistic t = (d̄ - μd) / (s_d / √n), where μd = 0 under the null hypothesis, n is the number of paired observations (10 in this case), and s_d is the standard deviation of the differences. Compute the t-value.
5. Step 5: Compare the calculated t-value to the critical t-value from the t-distribution table at α = 0.20 with degrees of freedom df = n - 1 (df = 9). If the absolute value of the t-value exceeds the critical value, reject the null hypothesis. Otherwise, fail to reject the null hypothesis. Interpret the decision in the context of the original claim.

Key Concepts

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about population parameters based on sample data. It involves formulating a null hypothesis (H0) and an alternative hypothesis (H1), then using sample statistics to determine whether to reject H0. In this context, the null hypothesis would state that there is no difference in passing play percentages between home and away games.

Dependent Samples

Dependent samples refer to pairs of observations that are related or matched in some way, such as measurements taken from the same subjects under different conditions. In this case, the passing play percentages for home and away games are dependent because they come from the same teams. This relationship affects the choice of statistical tests used to analyze the data.

Significance Level (α)

The significance level, denoted as α, is the threshold for determining whether to reject the null hypothesis in hypothesis testing. It represents the probability of making a Type I error, which occurs when the null hypothesis is incorrectly rejected. In this scenario, α is set at 0.20, indicating a willingness to accept a 20% chance of concluding that there is a difference in passing play percentages when there is none.