College

We appreciate your visit to The mean height of all adult American males is 69 inches 5 ft 9 in A researcher wants to prove that young American males between. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

The mean height of all adult American males is 69 inches (5 ft 9 in). A researcher wants to prove that young American males between the ages of 18 and 21 tend to be taller than 69 inches. A random sample of 100 young American males ages 18 to 21 yielded a sample mean of 71 inches.

(Here, [tex]\mu[/tex] represents the population mean height of young American males.)

Choose the correct hypotheses:

A. [tex]H_0: \mu = 69, \quad H_A: \mu \neq 69[/tex]

B. [tex]H_0: \mu \ \textgreater \ 69, \quad H_A: \mu \ \textless \ 69[/tex]

C. [tex]H_0: \bar{x} = 69, \quad H_A: \bar{x} \ \textgreater \ 69[/tex]

D. [tex]H_0: \mu = 69, \quad H_A: \mu \ \textgreater \ 69[/tex]

E. [tex]H_0: \mu = 71, \quad H_A: \mu \ \textless \ 71[/tex]

F. [tex]H_0: \bar{x} = 71, \quad H_A: \bar{x} \ \textless \ 71[/tex]

Answer :

To determine the appropriate hypothesis for the researcher's study, we need to understand what the researcher is trying to prove and set up our null and alternative hypotheses accordingly.

Here’s a step-by-step approach to solve the problem:

1. Understand the Null and Alternative Hypotheses:
- The null hypothesis (H₀) is a statement of no effect or no difference. It's what we assume to be true until we have evidence suggesting otherwise.
- The alternative hypothesis (Hₐ) is what the researcher wants to prove. It's a statement that indicates some effect or difference.

2. Identify What the Researcher Wants to Prove:
- The researcher wants to show that young American males (ages 18 to 21) tend to be taller than the mean height of all adult American males, which is 69 inches.

3. Set Up the Hypotheses:
- The null hypothesis (H₀) should reflect the status quo or no effect, which is that the mean height of young American males is equal to the population mean height of all adult American males.
- The alternative hypothesis (Hₐ) should reflect the researcher’s claim, which is that the mean height of young American males is greater than 69 inches.

4. Choose the Correct Set of Hypotheses:
- Based on the researcher's goal to prove "greater than," the proper formulation is:
- H₀: μ = 69 (The mean height of young American males is 69 inches.)
- Hₐ: μ > 69 (The mean height of young American males is greater than 69 inches.)

From this step-by-step reasoning, the correct choice is:

- D: H₀: μ = 69, Hₐ: μ > 69

This set of hypotheses correctly addresses the researcher's aim to prove that the average height of young males is greater than the overall average height of all adult males.

Thanks for taking the time to read The mean height of all adult American males is 69 inches 5 ft 9 in A researcher wants to prove that young American males between. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada