# 8.2 A single population mean using the student t distribution  (Page 3/21)

 Page 3 / 21

## Try it

You do a study of hypnotherapy to determine how effective it is in increasing the number of hourse of sleep subjects get each night. You measure hours of sleep for 12 subjects with the following results. Construct a 95% confidence interval for the mean number of hours slept for the population (assumed normal) from which you took the data.

8.2; 9.1; 7.7; 8.6; 6.9; 11.2; 10.1; 9.9; 8.9; 9.2; 7.5; 10.5

(8.1634, 9.8032)

The Human Toxome Project (HTP) is working to understand the scope of industrial pollution in the human body. Industrial chemicals may enter the body through pollution or as ingredients in consumer products. In October 2008, the scientists at HTP tested cord blood samples for 20 newborn infants in the United States. The cord blood of the "In utero/newborn" group was tested for 430 industrial compounds, pollutants, and other chemicals, including chemicals linked to brain and nervous system toxicity, immune system toxicity, and reproductive toxicity, and fertility problems. There are health concerns about the effects of some chemicals on the brain and nervous system. [link] shows how many of the targeted chemicals were found in each infant’s cord blood.

 79 145 147 160 116 100 159 151 156 126 137 83 156 94 121 144 123 114 139 99

Use this sample data to construct a 90% confidence interval for the mean number of targeted industrial chemicals to be found in an in infant’s blood.

## Solution b

Enter the data as a list.
Press `STAT` and arrow over to `TESTS` .
Arrow down to `8:TInterval` and press `ENTER` (or you can just press `8` ). Arrow to Data and press `ENTER` .
Arrow down to `List` and enter the list name where you put the data.
Arrow down to `Freq` and enter 1.
Arrow down to `C-level` and enter 0.90
Arrow down to `Calculate` and press `ENTER` .
The 90% confidence interval is (117.41, 137.49).

## Try it

A random sample of statistics students were asked to estimate the total number of hours they spend watching television in an average week. The responses are recorded in [link] . Use this sample data to construct a 98% confidence interval for the mean number of hours statistics students will spend watching television in one week.

 0 3 1 20 9 5 10 1 10 4 14 2 4 4 5

## Solution b

Enter the data as a list.
Press `STAT` and arrow over to `TESTS` .
Arrow down to `8:TInterval` .
Press `ENTER` .
Arrow to `Data` and press `ENTER` .
Arrow down and enter the name of the list where the data is stored.
Enter `Freq` : 1
Enter `C-Level` : 0.98
Arrow down to `Calculate` and press `Enter` .
The 98% confidence interval is (2.3965, 9,8702).

## References

“America’s Best Small Companies.” Forbes, 2013. Available online at http://www.forbes.com/best-small-companies/list/ (accessed July 2, 2013).

Data from Microsoft Bookshelf .

Data from http://www.forbes.com/.

“Disclosure Data Catalog: Leadership PAC and Sponsors Report, 2012.” Federal Election Commission. Available online at http://www.fec.gov/data/index.jsp (accessed July 2,2013).

“Human Toxome Project: Mapping the Pollution in People.” Environmental Working Group. Available online at http://www.ewg.org/sites/humantoxome/participants/participant-group.php?group=in+utero%2Fnewborn (accessed July 2, 2013).

Just a test from gplay
how come 5.67
by dividing 11.37 on 2
saifuddin
by dividing 11.34 on 2
saifuddin
what is index number?
vinayak
What is the differences between quota an lottery system of sampling
EGBE
What are the are the characteristics that are critically expedients in selecting the sample size
EGBE
fit a binomial distribution for the following data and test the goodness of fit x: 0 1 2 3 4 5 6 f: 5 18 28 12 7 6 4
solution
Mano
Mano
Simonsakala
It is a square chi
Nelson
But can't be a binomial because, the x numbers are 0 to 6, instead those would be "0" or "1" in a straight way
Nelson
You can do a chi-square test, but the assumption has to be a normal distribution, and the last f's number need to be "64"
Nelson
sorry the last f's numbers : "6 and 4" which are the observed values for 5 and 6 (expected values)
Nelson
hi
rajendra
can't understand basic of statistics ..
rajendra
Sorry I see my mistake, we have to calculate the expected values
Nelson
So we need this equation: P= (X=x)=(n to x) p^x(1-p)^n-x
Nelson
why it is not possible brother
ibrar
were n= 2 ( binomial) x= number of makes (0 to 6) and p= probability, could be 0.8.
Nelson
so after we calculate the expected values for each observed value (f) we do the chi-square. x^2=summatory(observed-expected)^2 / expected and compare with x^2 in table with 0.8
Nelson
tomorrow I'll post the answer, I'm so tired today, sorry for my mistake in the first messages.
Nelson
It is possible, sorry for my mistake
Nelson
two trader shared investment and buoght Cattle.Mr.Omer bought 255 cows & rented the farm for a period of 32 days. Mr. Ahmed grazed his Cattle for 25 days. Mr. Ahmed's cattle was 180 cows.Together they profited \$ 7800. the rent of the farm is \$ 3000 so divide the profit per gows/day for grazing day
Mohamed
how to start this book, who is reading thins first time
It is my first time reading this book
Good one
ihsan
from were did you get 2/50?m
People living longer
Why do you think that is?
Jazzy
because there is an increase in number of people with age more than 30.
Ok. And what do you think is the driving factor behind that hypothesis?
Jazzy
fewer birth and increase in # of years living or fewer dying
What about the improvement of technology and medicine?
Jazzy
hi,why the mean =sum(xi)/n but the variance =sum(xi-xbar)/ n-1 what is the difference between (n or n-1)
This is hard to type, so I'll use "m" for "x bar", and a few other notations that I hope will be clear: Definition: sqrt(SUM[(x - m)^2] / (n-1)) where m = SUM[x] / n Desired formula: sqrt((SUM[x^2] - SUM[x]^2)/n / (n-1)) Now let's do what you started to do, and see if we can manipulate the definitio
Michael
what is the difference between (n ) and (n-1) in the mean and variance
Soran
Definition: sqrt(SUM[(x - m)^2] / (n-1)) where m = SUM[x] / n what is the difference between (n and n-1)
Soran
Hi, the diference is tha when we estimate parameters in a sample (not in the total population) we need to consider the degrees of liberty for the estimation.
Nelson
Hie guys, am analysing rainfall data for different stations and i got kurtosis values of 0.7 for one station and 0.4 for another, what can i say about this?
Kudakwashe
hi
ujjal
difference in degrees of freedom
vinayak
who introduced the statistics in england
what year is data first used
Sunday
Gottfried achievell is a professor at
hi
Soran
hello
mskinne4
hi
Raja
hello
Tshepo
freakin annoying chat. uninstalled
KickingtheDonksNuts
Hi
Sunday
hello
Inoxent
Hello rumiex
Abimbola
How is ur day going
Abimbola
Pls I hv a question 🙋 to ask
Abimbola
I want to ask, as a student who wants to study mechatronic engineering in the University. What are the necessary subject he or she needed, and after ur service were can or she work as a graduate
Abimbola
?
Abimbola
hello
Gh
Write a short note on skewness
and on kurtosis too
Hiren
What is events
IT occurs in probability
Peter
yes
Preeti
any experiment done
Preeti
who introduced statistics in england
Sunday
who is a strong man?
who never gives up
Preeti
Who eats lots of food 😂
abhinav
A man with great physical strength
Nucks
Mustapha
hi
Samuel
hlw
Suman
hy
ibrar
One who withstand everything that was meant to break him.
Jazzy
"The stronger is not he who puts down his opponent on the ground but the stronger is he who controls himself in a pit of anger" (Bukhari Sharif)
saifuddin
still contemplating about analyzing statistical methods
solomon
Can you sir plz provide all the multiple choice questions related to Index numbers.?
about probabilty i have some questions and i want the solution
What is hypothesis?
its a scientific guess
ted
A hypothesis in a scientific context, is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon. In a scientific experiment or study, the hypothesis is a brief summation of the researcher's prediction of the study's findings.
Hamzah
Which may be supported or not by the outcome. Hypothesis testing is the core of the scientific method.
Hamzah
statistics means interpretation analysis and representation of numerical data
Ramzan
To check the statment or assumption about population parameter is xalled hypothesis
Ali
hypothesis is simply an assumption
Patrick