Question
The data set (75, 85, 58, 72, 70, 75) is a random sample from the normal distribution No(µ, σ). Determine a 95% two-sided confidence interval for the mean µ .
162
likes810 views
Answer to a math question The data set (75, 85, 58, 72, 70, 75) is a random sample from the normal distribution No(µ, σ). Determine a 95% two-sided confidence interval for the mean µ .
Brice
4.8113 Answers
To calculate a 95% two-sided confidence interval for the mean µ, we need to use the formula:
Confidence interval = Mean ± (critical value * standard deviation / √n)
First, we need to calculate the critical value for a 95% confidence interval. Since it is a two-sided confidence interval, we need to find the z-value for (1 - (1 - 0.95)/2) = 0.975 in the standard normal distribution.
Using a standard normal distribution table or a calculator, the z-value for a 95% confidence interval is approximately 1.96.
Next, we need to calculate the mean and standard deviation of the given data set.
Mean (µ) = (75 + 85 + 58 + 72 + 70 + 75) / 6 = 72.5
Standard Deviation (σ) = 8.8
Now, we can plug the values into the confidence interval formula:
Confidence interval = 72.5± (1.96 * 8.8/ √6) = 72.5± 7.04
Therefore, the 95% two-sided confidence interval for the mean µ is approximately (65.46, 79.54).
Frequently asked questions (FAQs)
Math question: Find the missing side length in a triangle with angle A = 60°, side a = 5, and side b = 8.
+
What is the standard deviation of a data set 8, 12, 9, 6, 15?
+
What is the value of sine(45°) according to the unit circle chart?
+
New questions in Mathematics