Question

# A simple random sample of 10 observations is derived from a normally distributed population with a...

A simple random sample of 10 observations is derived from a normally distributed population with a known standard deviation of 2.1. [Use Excel instead of the z table.]

a.
Is the condition that X−X− is normally distributed satisfied?

_Yes

_No

b. Compute the margin of error with 99% confidence. (Round intermediate calculations to at least 4 decimal places. Round "z" value to 3 decimal places and final answer to 2 decimal places.)

c. Compute the margin of error with 95% confidence. (Round intermediate calculations to at least 4 decimal places. Round "z" value to 3 decimal places and final answer to 2 decimal places.)

d. Which of the two margins of error will lead to a wider interval?

_The margin of error with 99% confidence.

_The margin of error with 95% confidence.

Solution :

(a)

Yes

(b)

Z/2 = 2.576

Margin of error = E = Z/2* ( /n)

= 2.576 * (2.1 / 10)

= 1.71

(c)

Z/2 = 1.96

Margin of error = E = Z/2* ( /n)

= 1.96 * (2.1 / 10)

= 1.30

(d)

The margin of error with 99% confidence.

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