Math Problem Statement

According to Abyss Consulting, the average age of viewers of “America’s Got Talent” is 25 years old. However, the producer of the show thinks it is higher than 25. Write the null hypothesis Ho and alternative hypothesis Ha

Solution

The null hypothesis (H0H_0) and the alternative hypothesis (HaH_a) for this scenario would be:

  • Null Hypothesis ( H0H_0 ): The average age of viewers of "America's Got Talent" is 25 years old. H0:μ=25H_0: \mu = 25

  • Alternative Hypothesis ( HaH_a ): The average age of viewers of "America's Got Talent" is greater than 25 years old. Ha:μ>25H_a: \mu > 25

Here, μ\mu represents the population mean age of the viewers.

Would you like to go over how to test these hypotheses using a statistical test like a t-test? Let me know if you'd like more details or have any questions.

Additional Related Questions:

  1. What is the difference between a one-tailed and two-tailed hypothesis test?
  2. How do you calculate the test statistic for a hypothesis test?
  3. What assumptions are made when performing a hypothesis test for the mean?
  4. How would you interpret the results if we reject the null hypothesis?
  5. What role does sample size play in hypothesis testing?

Tip: When forming hypotheses, remember that the null hypothesis generally represents the "status quo" or a claim of no difference, while the alternative hypothesis represents what you are trying to prove or test.

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Statistical Inference
Population Mean
One-Tailed Test

Formulas

H0: μ = 25
Ha: μ > 25

Theorems

Hypothesis Testing Theorem
One-Tailed Test

Suitable Grade Level

Grades 10-12