The student will calculate confidence intervals for means when the population standard deviation is unknown.

Given

The following real data are the result of a random survey of 39 national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let
$X=$ the number of colors on a national flag.

X

Freq.

1

1

2

7

3

18

4

7

5

6

Calculating the confidence interval

Calculate the following:

$\overline{x}=$

${s}_{x}=$

$n=$$$

3.26

1.02

39

Define the Random Variable,
$\overline{X}$ , in words.
$\overline{X}=$$\text{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$

the mean number of colors of 39 flags

What is
$\overline{x}$ estimating?

$\mu $

Is
${\sigma}_{x}$ known?

No

As a result of your answer to (4), state the exact distribution to use when calculating the Confidence Interval.

${t}_{\text{38}}$

Confidence interval for the true mean number

Construct a 95% Confidence Interval for the true mean number of colors on national flags.

How much area is in both tails (combined)?
$\alpha =$

0.05

How much area is in each tail?
$\frac{\alpha}{2}=$

0.025

Calculate the following:

lower limit =

upper limit =

error bound =

2.93

3.59

0.33

The 95% Confidence Interval is:

2.93; 3.59

Fill in the blanks on the graph with the areas, upper and lower limits of the Confidence Interval and the sample mean.

In one complete sentence, explain what the interval means.

Discussion questions

Using the same
$\overline{x}$ ,
${s}_{x}$ , and level of confidence, suppose that
$n$ were 69 instead of 39. Would the error bound become larger or smaller? How do you know?

Using the same
$\overline{x}$ ,
${s}_{x}$ , and
$n=\text{39}$ , how would the error bound change if the confidence level were reduced to 90%? Why?

The nanotechnology is as new science, to scale nanometric

brayan

nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale

Damian

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?