AP Statistics 4.4: Mean Test Hypotheses

State null and alternative hypotheses for a one-sample mean or mean difference, matching the equality and direction to the claim.

According to a 2017 national survey in Country B, the mean number of bedrooms in newly built

houses was 2.9. Rodney, a researcher, believes the mean number of bedrooms in newly built

houses in the country was different in 2024 than it was in 2017. To investigate his belief, he took

a large random sample of newly built houses in Country B in 2024 and recorded the number of

bedrooms in each house. The distribution of the number of bedrooms for the sampled houses is

summarized in the table.

Distribution of the Number of Bedrooms for the Houses Sampled in 2024

Table for Question 4.4.B—Identify the null and alternative hypotheses for a population mean or population mean difference with unknown σ question 1 — AP Statistics

Rodney will use a one-sample t-test for a population mean to test his belief.

In the context of Rodney's investigation, state the hypotheses for the test.

Model Solution
Let $\mu$ be the population mean number of bedrooms in newly built houses in 2024 in Country B.
$H_0:\mu=2.9,\qquad H_a:\mu\ne2.9.$

Scoring components
1. States the correct null equality with 2.9.
2. States the correct two-sided alternative.
3. Defines the population parameter with sufficient context.

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4.4.B—Identify the null and alternative hypotheses for a population mean or population mean difference with unknown σ question 1