Question

Margin of error (m.o.e.) is the same thing as the maximum error of the estimate (m.e.e.). There are two names for the same thing. (a)The z value for a 96.6% confidence interval estimate is A. 2.12 B. 1.82 C. 1.96 D. 2.00 (b) In developing a confidence interval for a population mean, a sample of 50 observations was used. The interval was determined to be 19.55 to 22.31. The margin of error (m.o.e.) for this interval is... A. 1.05 B. 1.38 C. 2.76 D. 4.22 (c) A confidence interval for a population mean was calculated to be 62.84 to 69.46. The population standard deviation was assumed to be 6.50, and a sample of 100 observations was used. What was the value of the sample mean used to create this interval? A. 56.34 B. 62.96 C. 66.15 D. 13.24

Answer 1

a) Given that, confidence level = 96.6%

A 96.6% of confidence level has significance level = 0.034

and critical value is ( from z-table)

Answer: A) 2.12

b) Given that, confidence interval is, ( 19.55 , 22.31)

where, lower limit = 19.55 and upper limit = 22.31

we want to fid, margin of error ( E ),

Answer:B) 1.38

c) Given that, confidence interval is, ( 62.84, 69.46)

where, lower limit = 62.84 and upper limit = 69.46

we want to find, sample mean

Answer: C) 66.15