A camp director is interested in the mean number of letters each child sends during his/her camp session. The population standard deviation is known to be 2.5. A survey of 20 campers is taken. The mean from the sample is 7.9 with a sample standard deviation of 2.8.
$\overline{x}=\text{\_\_\_\_\_\_\_\_}$
$\sigma =\text{\_\_\_\_\_\_\_\_}$
${s}_{x}=\text{\_\_\_\_\_\_\_\_}$
$n=\text{\_\_\_\_\_\_\_\_}$
$n-1=\text{\_\_\_\_\_\_\_\_}$
Define the Random Variables
$X$ and
$\overline{X}$ , in words.
Which distribution should you use for this problem? Explain your choice.
Construct a 90% confidence interval for the population mean number of letters campers send home.
State the confidence interval.
Sketch the graph.
Calculate the error bound.
What will happen to the error bound and confidence interval if 500 campers are surveyed? Why?
Stanford University conducted a study of whether running is healthy for men and women over age 50. During the first eight years of the study, 1.5% of the 451 members of the 50-Plus Fitness Association died. We are interested in the proportion of people over 50 who ran and died in the same eight–year period.
Define the Random Variables
$X$ and
$P\text{'}$ , in words.
Which distribution should you use for this problem? Explain your choice.
Construct a 97% confidence interval for the population proportion of people over 50 who ran and died in the same eight–year period.
State the confidence interval.
Sketch the graph.
Calculate the error bound.
Explain what a “97% confidence interval” means for this study.
In a recent sample of 84 used cars sales costs, the sample mean was $6425 with a standard deviation of $3156. Assume the underlying distribution is approximately normal.
Which distribution should you use for this problem? Explain your choice.
Define the Random Variable
$\overline{X}$ , in words.
Construct a 95% confidence interval for the population mean cost of a used car.
State the confidence interval.
Sketch the graph.
Calculate the error bound.
Explain what a “95% confidence interval” means for this study.
${t}_{\text{83}}$
mean cost of 84 used cars
CI: (5740.10, 7109.90)
EB = 684.90
A telephone poll of 1000 adult Americans was reported in an issue of
Time Magazine . One of the questions asked was “What is the main problem facing the country?” 20% answered “crime”. We are interested in the population proportion of adult Americans who feel that crime is the main problem.
Define the Random Variables
$X$ and
$P\text{'}$ , in words.
Which distribution should you use for this problem? Explain your choice.
Construct a 95% confidence interval for the population proportion of adult Americans who feel that crime is the main problem.
State the confidence interval.
Sketch the graph.
Calculate the error bound.
Suppose we want to lower the sampling error. What is one way to accomplish that?
The sampling error given by Yankelovich Partners, Inc. (which conducted the poll) is ± 3%. In 1-3 complete sentences, explain what the ± 3% represents.
Refer to the above problem. Another question in the poll was “[How much are] you worried about the quality of education in our schools?” 63% responded “a lot”. We are interested in the population proportion of adult Americans who are worried a lot about the quality of education in our schools.
Define the Random Variables
$X$ and
$P\text{'}$ , in words.
Which distribution should you use for this problem? Explain your choice.
Construct a 95% confidence interval for the population proportion of adult Americans worried a lot about the quality of education in our schools.
State the confidence interval.
Sketch the graph.
Calculate the error bound.
The sampling error given by Yankelovich Partners, Inc. (which conducted the poll) is ± 3%. In 1-3 complete sentences, explain what the ± 3% represents.
Six different national brands of chocolate chip cookies were randomly selected at the supermarket. The grams of fat per serving are as follows: 8; 8; 10; 7; 9; 9. Assume the underlying distribution is approximately normal.
Calculate a 90% confidence interval for the population mean grams of fat per serving of chocolate chip cookies sold in supermarkets.
State the confidence interval.
Sketch the graph.
Calculate the error bound.
If you wanted a smaller error bound while keeping the same level of confidence, what should have been changed in the study before it was done?
Go to the store and record the grams of fat per serving of six brands of chocolate chip cookies.
Calculate the mean.
Is the mean within the interval you calculated in part (a)? Did you expect it to be? Why or why not?
A confidence interval for a proportion is given to be (– 0.22, 0.34). Why doesn’t the lower limit of the confidence interval make practical sense? How should it be changed? Why?
Try these multiple choice questions.
The next three problems refer to the following: According to a Field Poll, 79% of California adults (actual results are 400 out of 506 surveyed) feel that “education and our schools” is one of the top issues facing California. We wish to construct a 90% confidence interval for the true proportion of California adults who feel that education and the schools is one of the top issues facing California. (Source: http://field.com/fieldpollonline/subscribers/)
A point estimate for the true population proportion is:
0.90
1.27
0.79
400
C
A 90% confidence interval for the population proportion is:
(0.761, 0.820)
(0.125, 0.188)
(0.755, 0.826)
(0.130, 0.183)
A
The error bound is approximately
1.581
0.791
0.059
0.030
D
The next two problems refer to the following:
A quality control specialist for a restaurant chain takes a random sample of size 12 to check the amount of soda served in the 16 oz. serving size. The sample mean is 13.30 with a sample standard deviation of 1.55. Assume the underlying population is normally distributed.
Find the 95% Confidence Interval for the true population mean for the amount of soda served.
(12.42, 14.18)
(12.32, 14.29)
(12.50, 14.10)
Impossible to determine
B
What is the error bound?
0.87
1.98
0.99
1.74
C
What is meant by the term “90% confident” when constructing a confidence interval for a mean?
If we took repeated samples, approximately 90% of the samples would produce the same confidence interval.
If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the sample mean.
If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean.
If we took repeated samples, the sample mean would equal the population mean in approximately 90% of the samples.
C
The next two problems refer to the following:
Five hundred and eleven (511) homes in a certain southern California community are randomly surveyed to determine if they meet minimal earthquake preparedness recommendations. One hundred seventy-three (173) of the homes surveyed met the minimum recommendations for earthquake preparedness and 338 did not.
Find the Confidence Interval at the 90% Confidence Level for the true population proportion of southern California community homes meeting at least the minimum recommendations for earthquake preparedness.
(0.2975, 0.3796)
(0.6270, 6959)
(0.3041, 0.3730)
(0.6204, 0.7025)
C
The point estimate for the population proportion of homes that do not meet the minimum recommendations for earthquake preparedness is:
0.6614
0.3386
173
338
A
Questions & Answers
Is there any normative that regulates the use of silver nanoparticles?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?