# Confidence Interval & Margin of Error

Please help with the following:

1. Of 515 Broiler chickens purchased from various kinds of food stores in different regions of a country and tested for types of bacteria that cause food borne illnesses 85% were infected with a particular bacterium.

A) Construct a 90% confidence interval? The 90% confidence interval is from ____% to _____%

B) Explain what your confidence interval says about chicken sold in the country

C) A government spokesperson claimed that the sample size was too small, relative to the billions of chickens slaughtered each year to generalize. Is this criticism valid?

2. A poll taken this year asked 1031 adults whether they were fans of a particular sport and 36% said they were. Last year 31% of a similar size sample had reported being fans of the sport.

A) Find the margin of error for the poll taken this year if one wants 95% confidence in the estimate of the percentage of adults who are fans of the sport.

ME=_______(Round to the three decimal places as needed

B) Explain what the margin of error means

C) If one wanted to be ((% confident instead of 95% confident would the margin of error be larger or smaller?

D) Find the margin of error for the poll taken this year if one wants 99% confidence in the estimate of the percent of adults who are fans of the sport.

E) In general if all other aspects of the situation remain the same will smaller margins of error produce greater or less confidence in the interval?

3. A Philanthropic organization sent free mailing labels and greeting cards to random sample of 100,000 potential donors on their mailing list and received 5247 donations.

A) Give a 90% confidence interval for the true proportion of those from their entire mailing list who may donate. The 90% confidence interval is from _____% to ______%

B) A staff member thinks that the true rate is 5.2%. Given the confidence interval you found, do you find that rate plausible?

4. An insurance company check police records on 597 accidents selected at random and notes that teenagers were at the wheel in 85 of them.

A) Construct the 95% confidence interval for the percentage of all auto accidents that involve teenage drivers. 95% CI= (_____%,_____%) (Round to one decimal place as needed)

B) Explain what your intervals means.

C) Explain what 95% confidence means

D) A politician urging tighter restrictions on drivers licenses issued to teens says,"in one of every five auto accidents a teenager is behind the wheel". Does the confidence interval support or contradict this statement?

https://brainmass.com/math/probability/confidence-interval-margin-error-592799

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#### Solution Summary

The solution provides step by step method for the calculation of confidence interval for population proportion and margin of error. Formula for the calculation and Interpretations of the results are also included.

Student Earnings: Confidence intervals and margins of error

6. Salaries: Student services consider college officials in admissions, registration, counseling, financial aid, campus ministry, food service, and so on. How much money do these people make each year? Suppose you read in your local newspaper that 45 officials in student services earned an average of = $50,340 each year.

a. Assume that x= $16,920 for salaries of college officials in student services. Find a 90'% confidence interval for the population mean salary of such personnel. What is the margin of error?

b. Assume that x= $10,780 for salaries of college officials in student services. Find a 90'% confidence interval for the population mean salary of such personnel. What is the margin of error?

c. Assume that x= $4830 for salaries of college officials in student services. Find a 90'% confidence interval for the population mean salary of such personnel. What is the margin of error?

d. Compare the margins of error for parts (a) through (c). As the standard deviation decreases,, does the margin of error decrease?

e. Compare the lengths of the confidence intervals for parts (a) through (c). As the standard deviation decreases, does the length of a 90% confidence interval decrease?

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