Mr. Guo receives many spam emails each day. A random sample of 12850 emails in his inbox indicates that 13 out of every 25 emails in his inbox is spam. (a) Find a reasonable point estimate for p. (b) Mr. Guo wishes to find a 97% confidence interval for p. Are all conditions for the Large-Sample Confidence Interval met? If not, explain why. (c) Find the z critical number associated with a 97% confidence in- terval. Hint: We are looking for z such that the central area is 97%. (d) Construct a central 97% confidence interval for p. (e) What is the minimum sample size required to conservatively es- timate p within .005 with 97% confidence?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section: Chapter Questions
Problem 8SGR
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2. Mr. Guo receives many spam emails each day. A random sample of
12850 emails in his inbox indicates that 13 out of every 25 emails in
his inbox is spam.
(a) Find a reasonable point estimate for p.
(b) Mr. Guo wishes to find a 97% confidence interval for p. Are all
conditions for the Large-Sample Confidence Interval met? If not,
explain why.
(c) Find the z critical number associated with a 97% confidence in-
terval. Hint: We are looking for z such that the central area is
97%.
(d) Construct a central 97% confidence interval for p.
(e) What is the minimum sample size required to conservatively es-
timate Р within .005 with 97% confidence?
Transcribed Image Text:2. Mr. Guo receives many spam emails each day. A random sample of 12850 emails in his inbox indicates that 13 out of every 25 emails in his inbox is spam. (a) Find a reasonable point estimate for p. (b) Mr. Guo wishes to find a 97% confidence interval for p. Are all conditions for the Large-Sample Confidence Interval met? If not, explain why. (c) Find the z critical number associated with a 97% confidence in- terval. Hint: We are looking for z such that the central area is 97%. (d) Construct a central 97% confidence interval for p. (e) What is the minimum sample size required to conservatively es- timate Р within .005 with 97% confidence?
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