Question

Confidence Intervals for a proportion and mean Do all steps in the confidence interval:

a) Check when easy the requirements for the interval (t-interval)

b) Create a summary of the information that goes into the interval

c) Write out the formula for the interval

d) Replace the symbols in the formula with the numbers from (b)

e) Produce the interval

f) Interpret the interval

In 1998, as an advertising campaign, the Nabisco Company announced a "1000 Chips Challenge," claiming that every 18-ounce bag of cookies contained at least 1000 chocolate chips. Students tested this by getting bags and counting. Create a 95% interval for the mean number of chocolate chips per bag.

1219	1214	1087	1200	1419	1121	1325	1345
1244	1258	1356	1132	1191	1270	1295	1135

An insurance company checks police records on 582 accidents selected at random and notes that teenagers were at the wheel in 91 of them. Create a 95% confidence interval for the percentage of all auto accidents that involve teenage drivers.

A company with a large fleet of cars hopes to keep gasoline costs down and sets a goal of attaining a fleet average of at least 26 miles per gallon. To see if the goal is being met, they check the gasoline usage for 50 company trips chosen at random, finding a mean of 25.02 mpg and a standard deviation of 4.83 mpg. Produce a 99% confidence interval for the average mpg.

A May 2007 Gallup Poll found that only 11% of a random sample of 1003 adults approved of attemps to clone a human. Produce a 90% confidence interval for the percentage of adults that approve of attempts to clone a human

The mayor of a small city suggested that the state locate a new prison there, arguing that the construction project and resulting jobs will be good for the local economy. A total of 2183 residents show up for a public hearing on the proposal, and a show of hands finds only 31 in favor of the prison project. What can the city council conclude about public support for the mayor's initiative? Produce a 98% confidence interval to answer the question.

Answer 1

Solution1:

here sample size is n=16

n<30 small sample

and population standard deviation not given .

we can go ahead with t interval

b) Create a summary of the information that goes into the interval

using R software

sample mean=xbar=1175.688

sample standard deviation=s= 271.9328

sample size=n=16

alpha=0.05

alpha/2=0.05/2=0.025

df=n-1=16-1=15

t critical=T.INV(0.025;15)=2.13145

c) Write out the formula for the interval

xbar-tc*s/sqrt(n),xbar+tc*s/sqrt(n)

d) Replace the symbols in the formula with the numbers from (b)

xbar-tc*s/sqrt(n),xbar+tc*s/sqrt(n)

1175.688-(2.13145)*(271.9328)/sqrt(16),1175.688+(2.13145)*(271.9328)/sqrt(16)

1030.785,1320.591

lower limit=1030.785

upper limit=1320.591

e) Produce the interval

1030.785<<1320.591

f) Interpret the interval

we are 95% confident that the true mean number of chocolate chips per bag lies in between

1031 and 1321(rounding to nearest integer)