Given the following information, determine the 68.3 percent, 95.5 percent, and 99.7 percent confidence intervals.
overbar above X equals 4.33 comma SE sub m equals 3
I've looked at the table as recommended. I just do not understand this at all. I'm really lost on this and confused. Pick a confidence level, calculate Z score do this do that. I am so lost and desperate to at least have a clue as to how this needs to be done. Help me someone please!!???
besides telling me to look at the back of a book for a table, looking at it does nothing for me I am lost. I would appreciate it.
Mean = 4.33
SE 3
1- a = .683
a= 0.317
Za/2 = Z0.1585 = 1 z table
invNorm(0.1585) = 1
mean -+ Z *SE
4.33 -1(3), 4.33+1*3
(1.33, 7.33)
You can follow concept and you will get rest of your answer.
Somebody be so kind and brake this down to me, please it's for a test I need the help.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability [(1-.95)/2] = Z = 1.96. You divide by 2, because you are considering both above and below.
95% = mean ± 1.96 SEm
The other percentages would be solved in the same way.
I understand that calculating confidence intervals can be confusing at first. I'll try my best to guide you through the steps.
To calculate confidence intervals, you need to know the sample mean (X̄), and the standard error (SE). In your case, you're given X̄ = 4.33 and SE = 3. We'll use the formulas:
68.3% Confidence Interval:
X̄ ± 1 * SE
95.5% Confidence Interval:
X̄ ± 1.96 * SE
99.7% Confidence Interval:
X̄ ± 2.57 * SE
Now let's calculate the confidence intervals step by step:
1. 68.3% Confidence Interval:
For a 68.3% confidence level, you'll use a Z-score of 1. The formula is:
X̄ ± 1 * SE
Plugging in the values, we get:
4.33 ± 1 * 3
This gives us a range from (4.33 - 3) to (4.33 + 3), resulting in a confidence interval of (1.33, 7.33).
2. 95.5% Confidence Interval:
For a 95.5% confidence level, you'll use a Z-score of 1.96. The formula is:
X̄ ± 1.96 * SE
Plugging in the values, we get:
4.33 ± 1.96 * 3
This gives us a range from (4.33 - 5.88) to (4.33 + 5.88), resulting in a confidence interval of (-1.55, 10.21).
3. 99.7% Confidence Interval:
For a 99.7% confidence level, you'll use a Z-score of 2.57. The formula is:
X̄ ± 2.57 * SE
Plugging in the values, we get:
4.33 ± 2.57 * 3
This gives us a range from (4.33 - 7.71) to (4.33 + 7.71), resulting in a confidence interval of (-3.38, 12.04).
Remember, these confidence intervals represent the range within which we can be certain that the true population mean lies with a given level of confidence.