Math Problem Statement

Adam tabulated the values for the average speed on each day of his road trip as 60.5, 63.2, 54.7, 51.6, 72.3, 70.7, 67.2, and 65.4 mph.

If Adam wanted to construct a one-sample t-statistic, what would the value for the degrees of freedom be?

Solution

To calculate the degrees of freedom (df) for a one-sample t-statistic, the formula is:

df=n1df = n - 1

Where nn is the number of observations.

Adam has recorded 8 values for the average speed:

n=8n = 8

Therefore, the degrees of freedom would be:

df=81=7df = 8 - 1 = 7

Thus, the degrees of freedom for Adam's one-sample t-statistic is 7.

Would you like a detailed explanation on how the t-statistic is used or any further clarifications?

Here are five related questions you might consider:

  1. How do you calculate a one-sample t-statistic?
  2. What is the interpretation of degrees of freedom in a t-test?
  3. How would you calculate the sample mean and standard deviation from the given data?
  4. What are the assumptions of the one-sample t-test?
  5. How do you interpret the results of a t-test?

Tip: In a t-test, the degrees of freedom impact the shape of the t-distribution, affecting the critical values used for hypothesis testing.

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Math Problem Analysis

Mathematical Concepts

Statistics
Degrees of Freedom
One-Sample T-Test

Formulas

Degrees of Freedom (df) = n - 1
One-Sample T-Statistic Formula

Theorems

T-Distribution

Suitable Grade Level

Grades 11-12, College Level