Question

In: Statistics and Probability

Consider a population having a standard deviation equal to 9.94. We wish to estimate the mean...

Consider a population having a standard deviation equal to 9.94. We wish to estimate the mean of this population.

(a) How large a random sample is needed to construct a 95 percent confidence interval for the mean of this population with a margin of error equal to 1? (Round your answer to the next whole number.)

The random sample is units.

(b) Suppose that we now take a random sample of the size we have determined in part a. If we obtain a sample mean equal to 345, calculate the 95 percent confidence interval for the population mean. What is the interval’s margin of error? (Round your answers to the nearest whole number.)

The 95 percent confidence interval is [, ] .

Margin of error

Expert Solution

Solution :

A ) Given that,

standard deviation = = 9.94

margin of error = E = 1

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.0025

Z_/2 = Z_0.0025 = 1.960

Sample size = n = ((Z_/2 * ) / E)²

= ((1.960 * 9.94) / 1)²

= 379.5639 = 380

Sample size = 380

B ) = 345

n = 380

= 9.94

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

Margin of error = E = Z_/2* ( $\sqrt$ /n)

= 1.960 * (9.94/ $\sqrt$ 380) = 0.99

Margin of error = 1

orchestra answered 2 years ago

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