Question
A radio station would like to estimate the proportion of listeners who heard and remembered a...
A radio station would like to estimate the proportion of listeners who heard and remembered a specific advertisement. How large a sample of listeners would the radio station need to take to estimate this proportion to within a margin of error of 0.08 (E = 0.08) using a 95% Confidence Level. The radio station has no guess of what the true proportion (p) actually is? n = [A]
Homework Answers
Answer #1
The following information has been provided:
Since no estimate of the population proportion p is provided, we use the estimate p = 0.5 (which corresponds to the worst-case scenario).
The critical value for the significance level α=0.05 is zc=1.96. The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error:
Therefore, the sample size needed to satisfy the condition
, and it must be an integer number, we conclude that the minimum
required sample size is
Let me know in the comments if anything is not clear. I will reply ASAP! Please do upvote if satisfied!
Not the answer you're looking for?
Similar Questions
A company is considering the purchase of advertising time on a local radio show and will...
A company is considering the purchase of advertising time on a
local radio show and will do so if it believes that the percent of
all radio listeners that listen to the show is greater than 30% =
0.30. To make this decision, the company randomly selects 120
regular radio listeners and asks each whether he or she listens to
the show. Of these 120 listeners, 42 report that they listen to the
show.
Estimate with 95 percent confidence the...
Suppose a hospital would like to estimate the proportion of patients who feel that physicians who...
Suppose a hospital would like to estimate the proportion of
patients who feel that physicians who care for them always
communicated effectively when discussing their medical care. A
pilot sample of 40 patients found that 18 reported that their
physician communicated effectively. Determine the additional number
of patients that need to be sampled to construct a 95% confidence
interval with a margin of error equal to 3% to estimate this
proportion.
Suppose a consumer advocacy group would like to conduct a survey to find the proportion p...
Suppose a consumer advocacy group would like to conduct a survey
to find the proportion p of consumers who bought the newest
generation of an MP3 player were happy with their purchase. How
large a sample n should they take to estimate p with 4% margin of
error and 95% confidence?
Q. Suppose a consumer advocacy group would like to conduct a survey to find the proportion...
Q. Suppose a consumer advocacy group would like to conduct a
survey to find the proportion p of consumers who bought the newest
generation of mobile phone were happy with their purchase.
(a) How large a sample n should they take to estimate p with 2%
margin of error and 90% confidence?
(b) The advocacy group took a random sample of 1000 consumers who
recently purchased this mobile phone and found that 400 were happy
with their purchase. Find
a...
A certain region would like to estimate the proportion of voters who intend to participate in...
A certain region would like to estimate the proportion of voters
who intend to participate in upcoming elections. A pilot sample of
25 voters found that 17 of them intended to vote in the election.
Determine the additional number of voters that need to be sampled
to construct a 96?% interval with a margin of error equal to 0.05
to estimate the proportion.
A certain region would like to estimate the proportion of voters who intend to participate in...
A certain region would like to estimate the proportion of voters
who intend to participate in upcoming elections. A pilot sample of
25 voters found that 21 of them intended to vote in the election.
Determine the additional number of voters that need to be sampled
to construct a 98?% interval with a margin of error equal to 0.04
to estimate the proportion.
A certain region would like to estimate the proportion of voters who intend to participate in...
A certain region would like to estimate the proportion of voters
who intend to participate in upcoming elections. A pilot sample of
25 voters found that 18 of them intended to vote in the election.
Determine the additional number of voters that need to be sampled
to construct a 96% interval with a margin of error equal to 0.07
to estimate the proportion.
A certain region would like to estimate the proportion of voters who intend to participate in...
A certain region would like to estimate the proportion of voters
who intend to participate in upcoming elections. A pilot sample of
25 voters found that 21 of them intended to vote in the election.
Determine the additional number of voters that need to be sampled
to construct a 94% interval with a margin of error equal to .04 to
estimate the proportion.
A college registrar wants to estimate the proportion of all students at the college who are...
A college registrar wants to estimate the proportion of all
students at the college who are dissatisfied with the online
registration procedure. What is the most conservative estimate of
the minimum sample size that would limit the margin of error to be
within 0.045 of the population proportion for a 95% confidence
interval?
What sample size of U.S. adults do you need, if you would like to estimate the...
What sample size of
U.S. adults do you need, if you would like to estimate the
proportion of U.S. adults who are "pro-choice" with a 2.5% margin
of error (at the 95% level)?
40
16
1,000
1,600
Your answer to the above question indicates that if you take a
sample of that size, the sample proportion of adults who are
pro-choice is:
More than 2.5% away from the proportion who are pro-choice
among all U.S. adults.
Within 2.5% of the...
ADVERTISEMENT
Need Online Homework Help?
Get Answers For Free
Most questions answered within 1 hours.
ADVERTISEMENT
Active Questions
asked 4 minutes ago
asked 15 minutes ago
asked 29 minutes ago
asked 29 minutes ago
asked 29 minutes ago
asked 53 minutes ago
asked 55 minutes ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago