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

likes

810 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 .

$Expert avatar$

Brice

4.8

113 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)

Question: Calculate the square root of 144 and find the square root value from the square root table.

Question: What is the y-coordinate of the point of intersection between the graphs of y = log(x) and y = log(x + 3) within the interval 0 < x < 10? (

What is the value of arccos(cos(π/4)) in radians?

New questions in Mathematics

Let 𝑢 = 𝑓(𝑥, 𝑦) = (𝑒^𝑥)𝑠𝑒𝑛(3𝑦). Check if 9((𝜕^2) u / 𝜕(𝑥^2)) +((𝜕^2) 𝑢 / 𝜕(𝑦^2)) = 0

Jose bought 3/4 of oil and his sister bought 6/8, which of the two bought more oil?

A book is between 400 and 450 pages. If we count them 2 at a time there is none left over, if we count them 5 at a time there is none left over and if we count them 7 at a time there are none left over, how many pages does the book have?

two particles start at the origin and move along the x axis. for 0 <= t <= 10, their respective position functions are given by x1 = cos(t) and x2 = (e^-3t) + 1. for how many values of t do the particles have the same velocity?

two pails of different sizes contain 34.5 litres of water altogether When 0.68 litre of water is poured from the bigger pail into the smaller pail the amount of water in the bigger pail is 9 times that in the smaller pail. How much water was in the smaller pail at first?

A, B, C and D are numbers; If ABCD = 23, What is the result of ABCD BCDA CDAB DABC operation?

4X^2 25