Do more than 50% of US adults get enough sleep? According to the Gallup organization's December 2004 Lifestyle Poll, 55% of US adults said that they get enough sleep. The poll was based on a random sample of 1003 adults. Test an appropriate hypothesis and state your conclusion in the context of the problem.

Null hypothesis:

Ho: p = .50 -->meaning: population proportion is equal to .50
Alternative hypothesis:
Ha: p > .50 -->meaning: population proportion is greater than .50

Using a formula for a binomial proportion one-sample z-test with your data included, we have:
z = (.55 - .50)/√(.50)(.50)/1003

Once you have the test statistic, you can go from there to draw your conclusions.

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.

To test whether more than 50% of US adults get enough sleep based on the Gallup organization's December 2004 Lifestyle Poll, we can set up the following hypothesis test:

Null hypothesis (H₀): p ≤ 0.5
Alternative hypothesis (H₁): p > 0.5

Where p represents the proportion of US adults who get enough sleep.

To test this hypothesis, we can use the z-test for proportions. The z-test formula is:
z = (p̂ - p₀) / sqrt((p₀ * (1 - p₀)) / n)

Where:
- p̂ represents the proportion of US adults who reported getting enough sleep in the sample.
- p₀ represents the hypothesized proportion (50% = 0.5).
- n represents the sample size (1003 adults).

According to the Gallup organization's poll, 55% of US adults reported getting enough sleep. So, p̂ = 0.55.

Plugging the values into the z-test formula:
z = (0.55 - 0.5) / sqrt((0.5 * (1 - 0.5)) / 1003)

Calculating this expression gives us the z-value.

Using a standard normal distribution table, we can find the critical value or the p-value associated with the obtained z-value. Comparing the critical value or p-value to a significance level (e.g., 0.05), we can assess whether there is sufficient evidence to reject the null hypothesis.

If the critical value is greater than the obtained z-value, or if the p-value is less than the significance level, we would reject the null hypothesis and conclude that more than 50% of US adults get enough sleep. Conversely, if the critical value is not greater than the obtained z-value, or if the p-value is greater than the significance level, we would fail to reject the null hypothesis.

It is necessary to conduct the calculations to find the results for reaching a conclusion.