To test the hypothesis and determine whether more than 50% of US adults get enough sleep, we can use a hypothesis test for a population proportion. Let's follow these steps:
Step 1: State the hypotheses.
The null hypothesis (H0): The proportion of US adults who get enough sleep is equal to or less than 50%.
The alternative hypothesis (Ha): The proportion of US adults who get enough sleep is greater than 50%.
Step 2: Set the significance level.
We need to set a significance level (alpha) to make decisions about the null hypothesis. Let's assume a significance level of 0.05, which is commonly used.
Step 3: Collect and analyze the data.
According to the Gallup organization's December 2004 Lifestyle Poll, 55% of the 1003 US adults sampled claimed that they get enough sleep.
Step 4: Determine the test statistic and calculate the p-value.
To perform the hypothesis test, we need to calculate the test statistic and the corresponding p-value. In this case, we will use the one-sample proportion z-test.
The test statistic is calculated using the formula:
z = (p - P0) / sqrt((P0 * (1 - P0)) / n)
Where:
p = sample proportion (55% in this case)
P0 = hypothesized proportion under the null hypothesis (50% in this case)
n = sample size (1003 in this case)
Calculating the test statistic, we have:
z = (0.55 - 0.50) / sqrt((0.50 * (1 - 0.50)) / 1003)
z ≈ 1.99
Using a standard normal distribution table or a statistical software, we can determine the p-value associated with a test statistic of 1.99.
Step 5: Make a decision.
Compare the p-value with the significance level (alpha) to make a decision about the null hypothesis. If the p-value is less than alpha (0.05), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
In this case, assuming our p-value is less than 0.05, we would reject the null hypothesis that the proportion of US adults who get enough sleep is equal to or less than 50%.
Therefore, in the context of the problem, we can conclude that based on the Gallup organization's December 2004 Lifestyle Poll, there is evidence to suggest that more than 50% of US adults get enough sleep.