SOLUTION: Find the minimum sample size n needed to estimate sigma for the given values of c, sigma ,and E. c = 0.98; sigma = 6.9 and E = 2 Assume that a preliminary sample has at least 30 me

Algebra ->  Probability-and-statistics -> SOLUTION: Find the minimum sample size n needed to estimate sigma for the given values of c, sigma ,and E. c = 0.98; sigma = 6.9 and E = 2 Assume that a preliminary sample has at least 30 me      Log On


   

Question 1193142: Find the minimum sample size n needed to estimate sigma for the given values of c, sigma ,and E. c = 0.98; sigma = 6.9 and E = 2 Assume that a preliminary sample has at least 30 members . n =___ ( Round up to the nearest whole number).
Answer by CPhill(1987) About Me  (Show Source):
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**1. Find the z-score for the given confidence level (c = 0.98)**
* Since c = 0.98, the alpha level (α) is 1 - 0.98 = 0.02.
* We need to find the z-score that corresponds to an area of 1 - α/2 = 0.99 in the standard normal distribution table.
* The z-score for 0.99 is approximately 2.33.
**2. Use the formula for sample size (n)**
* The formula to determine the minimum sample size (n) needed to estimate the population standard deviation (σ) with a given confidence level and margin of error (E) is:
n = (z * σ / E)²
where:
* n is the sample size
* z is the z-score corresponding to the desired confidence level
* σ is the population standard deviation
* E is the desired margin of error
* Substitute the given values:
n = (2.33 * 6.9 / 2)²
n = (16.077 / 2)²
n = 8.0385²
n ≈ 64.62
**3. Round up to the nearest whole number**
* Since we need a whole number of samples, round up n to 65.
**Therefore, the minimum sample size (n) needed to estimate sigma for the given values is 65.**