According to the United States Census Bureau, the average single-family home constructed in 2016 was 2,438 square feet. Carmen wondered if families in her area still want a smaller home in comparison to the average. She randomly selected 45 people and asked what the ideal square footage of a home is for them. From the responses, she calculated the sample mean equals 1,550 square feet with a sample standard deviation of 54 square feet. What are the competing hypotheses? A) H₀:$\mu$ $\neq$ 2,438;H_A$\mu$ = 2,438 B) H₀:$\mu$ $\neq$ 1,550; H_A$\mu$ = 1,550 C) H₀:$\mu$ $\ge$ 2,438; H_A$\mu$

Question

According to the United States Census Bureau, the average single-family home constructed in 2016 was 2,438 square feet. Carmen wondered if families in her area still want a smaller home in comparison to the average. She randomly selected 45 people and asked what the ideal square footage of a home is for them. From the responses, she calculated the sample mean equals 1,550 square feet with a sample standard deviation of 54 square feet. What are the competing hypotheses? A) H₀:$\mu$ $\neq$ 2,438;H_A$\mu$ = 2,438 B) H₀:$\mu$ $\neq$ 1,550; H_A$\mu$ = 1,550 C) H₀:$\mu$ $\ge$ 2,438; H_A$\mu$ < 2,438 D) H₀:$\mu$ = 1,550; H_A$\mu$ $\neq$ 1,550

Quizplus · Accepted Answer

Carmen is comparing the ideal square footage desired by families in her area to the national average from 2016, which is 2,438 square feet. Therefore, the null hypothesis (H0) should state there is no difference from the national average, and the alternative hypothesis (H1) should suggest that the ideal square footage is less than the national average, reflecting her interest in whether families prefer smaller homes.

According to the United States Census Bureau, the Average Single-Family μ\muμ

According to the United States Census Bureau, the Average Single-Family $\mu$