Consider a population with a known standard deviation of 15.4. In order to compu

Question

Consider a population with a known standard deviation of 15.4. In order to compute an interval estimate for the population mean, a sample of 35 observations is drawn. Use Table 1. a. Is the condition that X^- is normally distributed satisfied? Yes No b. Compute the margin of error at a 90% confidence level. (Round intermediate calculations to 4 decimal places. Round "z-value" to 3 decimal places and final answer to 2 decimal places. Margin of error ____ c. Compute the margin of error at a 90% confidence level based on a larger sample of 310 observations (Round intermediate calculations to 4 decimal places. Round "z-value" to 3 decimal places and final answer to 2 decimal places.) Margin of error ____ d. Which of the two margins of error will lead to a wider confidence interval? 90% confidence with n = 35. 90% confidence with n = 310.

Explanation / Answer

Answer to the question;

Standard deviation = 15.4
n = 35

a. Is Xbar normally distributed ?
Yes.

b. 90% ME = ?
Margin of error = Z*sigma/sqrt(n)
= (1.96*15.4)/(4/sqrt(35))
= 44.64

c.
90% ME = ?
Margin of error = Z*sigma/sqrt(n)
= (1.96*15.4)/(4/sqrt(310))
= 132.861

d. The one calc. in c. is wider.
90% CI with n=310

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