Question

In: Statistics and Probability

Suppose a sample has a sample mean of 53, a sample size of 40, and the...

Suppose a sample has a sample mean of 53, a sample size of 40, and the population has a standard deviation of 4. We want to calculate a 99% confidence interval for the population mean. The critical Z* in this case is 2.576. The confidence interval is (to one decimal place),

a. (42.7, 63.3)

b. (48.8, 57.2)

c. (49, 57)

d. (51.4, 54.6)

e. (52.4, 53.6)

f. (52.7, 53.3)

Solutions

Expert Solution

Solution :

Given that,

= 53

= 4

n = 40

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= 2.576 * (4 / $\sqrt$ 40 )

= 1.6

At 99% confidence interval estimate of the population mean is,

- E < < + E

53 - 1.6 < < 53 + 1.6

51.4 < < 54.6

(51.4, 54.6)

Option d ) is correct.

orchestra answered 1 year ago

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