Someone who has never seen a normal die before decides to estimate the mean value of all its faces (μ) by rolling it many times. First, they are told that the standard deviation is σ = 1.7. Then, they roll the die 50 times and get a sample mean of x-bar = 3.7. Finally, at the 95% confidence level, they calculate the margin of error to be E = 0.5. Which of the following is a correct interpretation for this result?
THERE IS A 95% CHANCE THAT THE MEAN FACES IS BETWEEN 3.2 AND 4.2
To interpret the given result, we need to understand the concepts of mean, standard deviation, sample mean, and margin of error.
The mean (μ) is the average value of all the faces of a normal die. It represents the expected central value.
Standard deviation (σ) measures the variability or spread of the values around the mean. In this case, the standard deviation is given as 1.7, which means the face values of the die usually deviate from the mean by about 1.7 units.
Sample mean (x-bar) is the average value calculated from a sample. In this case, the person rolled the die 50 times and obtained a sample mean of 3.7.
Margin of error (E) is the maximum difference between the sample mean and the true population mean. It takes into account the variability of the data and the desired confidence level. In this case, the margin of error is calculated as 0.5.
Now, let's interpret the result based on the information given:
At the 95% confidence level, the margin of error (E) is 0.5. This means that if the person were to repeat the experiment many times and calculate the sample mean each time, 95% of the time the true population mean would fall within a range of the sample mean plus or minus 0.5 units.
Therefore, a correct interpretation for this result would be: "With 95% confidence, we can estimate that the true mean value of all the faces of the die falls between 3.2 and 4.2 units."