Question

# Use the given information to find the minimum sample size required to estimate an unknown population...

Use the given information to find the minimum sample size required to estimate an unknown population mean

muμ.

How many students must be randomly selected to estimate the mean weekly earnings of students at one​ college? We want​ 95% confidence that the sample mean is within

​\$22

of the population​ mean, and the population standard deviation is known to be

​\$4343.

A.

1 comma 7761,776

B.

2 comma 5102,510

C.

1 comma 5651,565

D.

1 comma 251

Answer: How many students must be randomly selected to estimate the mean weekly earnings of students at one​ college? We want​ 95% confidence that the sample mean is within \$2 of the population​ mean, and the population standard deviation is known to be \$43.

Solution:

At 95%, α = 0.05

Zα/2 = 1.96

Margin of error, E = 2

Population standard deviation, σ = 43

Sample size, n:

n = (Zα/2 * σ / E)2

n = (1.96*43 / 2)2

n = 1775.7796

n = 1,776

The option A. is correct answer

Therefore, 1,776 students must be randomly selected to estimate the mean weekly earnings of students at one​ college.

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