A simple random sample of 32 observations is derived from a normally distributed

Question

A simple random sample of 32 observations is derived from a normally distributed population with a known standard deviation of 2.1. Use Table 1.

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

Compute the margin of error with 90% confidence. (Round intermediate calculations to 4 decimal places. Round "z-value" to 3 decimal places and final answer to 2 decimal places.)

A simple random sample of 32 observations is derived from a normally distributed population with a known standard deviation of 2.1. Use Table 1.

Explanation / Answer

Answer:

A simple random sample of 32 observations is derived from a normally distributed population with a known standard deviation of 2.1. Use Table 1.

a.

Is the condition that  is normally distributed satisfied?

Yes

No

b.

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

Margin of error = 1.96*2.1/sqrt(32) =

0.7276

  Margin of error=0.73

c.

Compute the margin of error with 90% confidence. (Round intermediate calculations to 4 decimal places. Round "z-value" to 3 decimal places and final answer to 2 decimal places.)

Margin of error = 1.645*2.1/sqrt(32) = 0.6107

  Margin of error=0.61

d.

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

Answer: The margin of error with 95% confidence.

The margin of error with 90% confidence.

A simple random sample of 32 observations is derived from a normally distributed population with a known standard deviation of 2.1. Use Table 1.

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