I need help on this one too. Any one willing to get me started? THANKS!
Potassium is a mineral that helps the kidneys function normally. It also plays a key role in cardiac, skeletal, and smooth muscle contraction, making it an important nutrient for normal heart, digestive, and muscular function. A test for the level of potassium in the blood is not perfectly precise. Moreover, the actual level of potassium in a person’s blood varies slightly from day to day. Normal levels of potassium range from 3.7 mEq/L to 5.2 mEq/L.
(Note mEq/L represents milliequivalents per liter – which is just a type of concentration measurement.)
a) What does the phrase “statistically significant” mean? Explain.
b) If nine measurements for Jason were taken on different days with levels (mEq/L) given by 3.6, 3.7, 5.1, 5.6, 5.4, 4.7, 4.6, 3.8, and 5.2 respectively what is a 95% confidence level for his mean potassium level?
c) Do you think his potassium levels are normal? Explain.
I'll give you some hints to get started, then let you take it from there.
For part a:
Statistically significant is meant to reflect the results of a statistical test when the null hypothesis is rejected.
For parts b & c:
Find the mean and standard deviation of the measurements given. You can then use a formula to calculate the 95% confidence interval using the mean, standard deviation, and sample size.
Thanks again....it helps me sort things out. K
a) To understand what the phrase "statistically significant" means, we need to understand the concept of null hypothesis and statistical testing. In statistical analysis, a null hypothesis is a statement that assumes there is no significant difference or relationship between variables. The purpose of a statistical test is to determine whether there is enough evidence to reject the null hypothesis and suggest that there is a significant difference or relationship.
When a result is deemed statistically significant, it means that the evidence gathered from the data is strong enough to reject the null hypothesis. In other words, it suggests that the observed difference or relationship between variables is unlikely to have occurred by chance alone.
b) To calculate the 95% confidence level for the mean potassium level, we need to follow these steps:
1. Find the mean of the measurements: Add up all the values (3.6 + 3.7 + 5.1 + 5.6 + 5.4 + 4.7 + 4.6 + 3.8 + 5.2) and divide by the total number of measurements (9).
2. Find the standard deviation: Calculate the differences between each measurement and the mean, square them, sum them up, divide by (n-1), and take the square root.
3. Calculate the standard error: Divide the standard deviation by the square root of the sample size.
4. Calculate the margin of error: Multiply the standard error by the critical value associated with a 95% confidence level (which can be found from a standard normal distribution table).
5. Construct the confidence interval: Subtract the margin of error from the mean to get the lower bound, and add the margin of error to the mean to get the upper bound.
c) To determine if Jason's potassium levels are normal, we need to compare his mean potassium level (calculated in part b) with the normal range provided in the question (3.7 mEq/L to 5.2 mEq/L). If the mean falls within this range, we can conclude that his potassium levels are normal. If the mean is below or above this range, we would consider it abnormal.
Remember, this analysis is based on a sample of measurements, and additional factors or medical consultations may be necessary to make a definitive determination about Jason's potassium levels.