Math Problem Statement

Sleep Awareness Week begins in the spring with the release of the National Sleep Foundauon's annual poll of U.S. sleep habits and ends with the beginning of daylight saving time, when most pe sle lose an hour of sleep. In the foundation's random imple of 1029 U.S. adults, 48% reported that the "often or always" got enough sleep during *he previous 7 nights. To determine if these data provide convincing evidence that few than half of all U.S. adults would say they often or always get enough sleep, 100 simulated SRSs of size n = 1029 were selected. Each dot in the graph shows the percentage of adults who said they often or always get enough sleep in a simulated SRS, assuming that each adult has a 50% chance of saying they often or always get enough sleep.

In the simulation, what percentage of the samples resulted in 48% or fewer of the adults saying they often or always go enough sleep? Provide your answer as a percent with precision as a whole number

Solution

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Simulations
Sampling
Probability

Formulas

(Number of samples ≤ 48%) / (Total simulations) × 100

Theorems

Central Limit Theorem
Law of Large Numbers

Suitable Grade Level

Grades 11-12, College Level