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Compute E, the margin of error for the Z interval, for a 95% confidence interval for m if a random sample of size n = 50 with a sample mean = 28 is drawn from a population with 𝜎  = 2.

Question

Compute E, the margin of error for the Z interval, for a 95% confidence interval for m if a random sample of size n = 50 with a sample mean = 28 is drawn from a population with 𝜎  = 2.

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Solution

To compute the margin of error (E) for a 95% confidence interval, we use the formula:

E = Z * (σ/√n)

Where:

  • Z is the Z-score, which corresponds to the desired confidence level. For a 95% confidence interval, the Z-score is approximately 1.96.
  • σ is the population standard deviation, which is given as 2.
  • n is the sample size, which is given as 50.

Substituting the given values into the formula, we get:

E = 1.96 * (2/√50)

Now, calculate the value inside the parenthesis:

2/√50 = 0.2828

Then, multiply this value by the Z-score:

E = 1.96 * 0.2828 = 0.554

So, the margin of error for the 95% confidence interval is approximately 0.554.

This problem has been solved

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