If you are using a student's-t distribution for a homework problem below, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
Among various ethnic groups, the standard deviation of heights is known to be approximately 3 inches. We wish to construct a 95% confidence interval for the mean height of male Swedes. 48 male Swedes are surveyed. The sample mean is 71 inches. The sample standard deviation is 2.8 inches.
$\overline{x}=$$\text{\_\_\_\_\_\_\_\_}$
$\sigma =$$\text{\_\_\_\_\_\_\_\_}$
${s}_{x}=$$\text{\_\_\_\_\_\_\_\_}$
$n=$$\text{\_\_\_\_\_\_\_\_}$
$n-1=$$\text{\_\_\_\_\_\_\_\_}$
Define the Random Variables
$X$ and
$\overline{X}$ , in words.
Which distribution should you use for this problem? Explain your choice.
Construct a 95% confidence interval for the population mean height of male Swedes.
State the confidence interval.
Sketch the graph.
Calculate the error bound.
What will happen to the level of confidence obtained if 1000 male Swedes are surveyed instead of 48? Why?
71
3
2.8
48
47
$N$$(\text{71},\frac{3}{\sqrt{\text{48}}})$
CI: (70.15,71.85)
EB = 0.85
In six packages of “The Flintstones® Real Fruit Snacks” there were 5 Bam-Bam snack pieces. The total number of snack pieces in the six bags was 68. We wish to calculate a 96% confidence interval for the population proportion of Bam-Bam snack pieces.
Define the Random Variables
$X$ and
$P\text{'}$ , in words.
Which distribution should you use for this problem? Explain your choice
Calculate
$p\text{'}$ .
Construct a 96% confidence interval for the population proportion of Bam-Bam snack pieces per bag.
State the confidence interval.
Sketch the graph.
Calculate the error bound.
Do you think that six packages of fruit snacks yield enough data to give accurate results? Why or why not?
A random survey of enrollment at 35 community colleges across the United States yielded the following figures (source:
Microsoft Bookshelf ): 6414; 1550; 2109; 9350; 21828; 4300; 5944; 5722; 2825; 2044; 5481; 5200; 5853; 2750; 10012; 6357; 27000; 9414; 7681; 3200; 17500; 9200; 7380; 18314; 6557; 13713; 17768; 7493; 2771; 2861; 1263; 7285; 28165; 5080; 11622. Assume the underlying population is normal.
$\overline{x}=$
${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 95% confidence interval for the population mean enrollment at community colleges in the United States.
State the confidence interval.
Sketch the graph.
Calculate the error bound.
What will happen to the error bound and confidence interval if 500 community colleges were surveyed? Why?
8629
6944
35
34
${t}_{\text{34}}$
CI: (6244, 11,014)
EB = 2385
It will become smaller
From a stack of
IEEE Spectrum magazines, announcements for 84 upcoming engineering conferences were randomly picked. The mean length of the conferences was 3.94 days, with a standard deviation of 1.28 days. Assume the underlying population is normal.
Define the Random Variables
$X$ and
$\overline{X}$ , in words.
Which distribution should you use for this problem? Explain your choice.
Construct a 95% confidence interval for the population mean length of engineering conferences.
State the confidence interval.
Sketch the graph.
Calculate the error bound.
Questions & Answers
what is variations in raman spectra for nanomaterials
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest.
Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.?
How this robot is carried to required site of body cell.?
what will be the carrier material and how can be detected that correct delivery of drug is done
Rafiq
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?
Source:
OpenStax, Collaborative statistics homework book: custom version modified by r. bloom. OpenStax CNX. Dec 23, 2009 Download for free at http://legacy.cnx.org/content/col10619/1.2
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