Do you drink the recommended amount of water each day? Most Americans don't! On average, Americans drink 5.4 eight-oz servings of water a day. A sample of 36 education professionals was randomly selected and their water consumption for a 24-hour period was monitored; the mean amount consumed was 46.8 oz. Assuming the amount of water consumed daily by adults is normally distributed and the standard deviation is 10.9 oz, is there sufficient evidence to show that education professionals consume, on average, more water daily than the national average? Use α = .05.
Multiply 5.4 by 8 to get in the same units.
Z = (score-mean)/SEm
SEm = SD/√n
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability for your Z score.
if your him department has 100,000 active medical records and you received 5352 request for records within a 6 month period, what is the request rate for the past 6 months? round to 2 decimal points.
To determine if there is sufficient evidence to show that education professionals consume, on average, more water daily than the national average, we can conduct a hypothesis test.
Step 1: State the hypotheses.
The null hypothesis (H0): The mean amount of water consumed by education professionals is equal to the national average.
The alternative hypothesis (Ha): The mean amount of water consumed by education professionals is greater than the national average.
Step 2: Set the significance level.
The significance level (α) is given as 0.05.
Step 3: Calculate the test statistic.
Since we have the sample mean (x̄ = 46.8 oz), sample standard deviation (s = 10.9 oz), sample size (n = 36), and the population standard deviation (σ = 10.9 oz), we can use the z-test.
The formula for the test statistic (z-score) is:
z = (x̄ - μ) / (σ / √n)
Where x̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
For this problem, the null hypothesis assumes that the population mean is equal to the national average (μ = 5.4 * 8 oz) and the alternative hypothesis assumes that the population mean is greater (μ > 5.4 * 8 oz).
So, the formula becomes:
z = (46.8 - 5.4 * 8) / (10.9 / √36)
Step 4: Determine the p-value.
We will calculate the p-value based on the z-score obtained in the previous step. The p-value represents the probability of obtaining a sample mean as extreme as the one observed, assuming the null hypothesis is true.
Step 5: Make a decision.
Compare the p-value with the significance level (α) to make a decision. If the p-value is less than α, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Step 6: State the conclusion.
Based on the decision in Step 5, state your conclusion in the context of the problem.
Now, let's calculate the test statistic and make a decision.
z = (46.8 - 5.4 * 8) / (10.9 / √36)
z = 2.18
Using a z-table or a calculator, we can find the corresponding p-value for z = 2.18. The p-value is the probability of observing a z-score as extreme as 2.18 or greater.
Assuming a one-tailed test (since we are interested in determining if education professionals consume more water daily than the national average), the p-value is found to be approximately 0.0157.
Since the p-value (0.0157) is less than the significance level (0.05), we reject the null hypothesis. There is sufficient evidence to show that education professionals consume, on average, more water daily than the national average.
In conclusion, the sample data suggests that education professionals consume more water on average than the national average.