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The error bound formula for a population mean when the population standard deviation is known is
EBM = ( z α 2 ) ( σ n ) .

The formula for sample size is n = z 2 σ 2 E B M 2 , found by solving the error bound formula for n .

In this formula, z is z α 2 , corresponding to the desired confidence level. A researcher planning a study who wants a specified confidence level and error bound can use this formula to calculate the size of the sample needed for the study.

The population standard deviation for the age of Foothill College students is 15 years. If we want to be 95% confident that the sample mean age is within two years of the true population mean age of Foothill College students, how many randomly selected Foothill College students must be surveyed?

  • From the problem, we know that σ = 15 and EBM = 2.
  • z = z 0.025 = 1.96, because the confidence level is 95%.
  • n = z 2 σ 2 E B M 2 = ( 1.96 ) 2 ( 15 ) 2 2 2 = 216.09 using the sample size equation.
  • Use n = 217: Always round the answer UP to the next higher integer to ensure that the sample size is large enough.

Therefore, 217 Foothill College students should be surveyed in order to be 95% confident that we are within two years of the true population mean age of Foothill College students.

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The population standard deviation for the height of high school basketball players is three inches. If we want to be 95% confident that the sample mean height is within one inch of the true population mean height, how many randomly selected students must be surveyed?

35 students

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“American Fact Finder.” U.S. Census Bureau. Available online at http://factfinder2.census.gov/faces/nav/jsf/pages/searchresults.xhtml?refresh=t (accessed July 2, 2013).

“Disclosure Data Catalog: Candidate Summary Report 2012.” U.S. Federal Election Commission. Available online at http://www.fec.gov/data/index.jsp (accessed July 2, 2013).

“Headcount Enrollment Trends by Student Demographics Ten-Year Fall Trends to Most Recently Completed Fall.” Foothill De Anza Community College District. Available online at http://research.fhda.edu/factbook/FH_Demo_Trends/FoothillDemographicTrends.htm (accessed September 30,2013).

Kuczmarski, Robert J., Cynthia L. Ogden, Shumei S. Guo, Laurence M. Grummer-Strawn, Katherine M. Flegal, Zuguo Mei, Rong Wei, Lester R. Curtin, Alex F. Roche, Clifford L. Johnson. “2000 CDC Growth Charts for the United States: Methods and Development.” Centers for Disease Control and Prevention. Available online at http://www.cdc.gov/growthcharts/2000growthchart-us.pdf (accessed July 2, 2013).

La, Lynn, Kent German. "Cell Phone Radiation Levels." c|net part of CBX Interactive Inc. Available online at http://reviews.cnet.com/cell-phone-radiation-levels/ (accessed July 2, 2013).

“Mean Income in the Past 12 Months (in 2011 Inflaction-Adjusted Dollars): 2011 American Community Survey 1-Year Estimates.” American Fact Finder, U.S. Census Bureau. Available online at http://factfinder2.census.gov/faces/tableservices/jsf/pages/productview.xhtml?pid=ACS_11_1YR_S1902&prodType=table (accessed July 2, 2013).

Questions & Answers

what is statistics
Bhavani Reply
statistics is the beach of mathematics which deals with collection ,organisation, presentation, analysis and interpretation of numerical data
oh but interpretation of data, like what and how? 🤔
interpretation: Think in a way that you have given a company year turnover and you have a record of 100years and data set is like (Year,Turnover). Now with that data you can interpret many thing how was the company growth, when were the losses and other things
interpretation: it is a process in which we make a decision about a population on the basis of sample data . example: if we want to interpret the average income of employees for upcoming year so we have to interpret the income of employees on the basis of previous year's income of those employees
thank you saeed, Akash. I understood.
Finding correlation and regression
Langat Reply
explain statistics whether it is a science or arts or both
ratnapriya Reply
I would say art is a creation. A chef is an artist. They create new dishes just like the painters. I believe one who creates something new, is an artist. So, Statistics is also an art, if you know it, you can create some new formula, theory, law, etcetera. It is also Science. So yes, it is both.
how do you use the normal distribution table when testing the hypothesis
I am sorry Davia, I cannot help you with that.
percentages of all the possible outcomes are measured. This is so simple and bases on the questionnaire or interview schedule. It's just measuring the probability chances of high %age of the either part of the hypothesis ... dependent ..independent. data is classified on the basis of respondents
what percent of the students would be expected to score above 95?
Peachy Reply
inferential statistics is what?
Seyi Reply
in which we make infrences (hypothsis)
surpose a data set of 2,3,5,6,1,4 are given find median
lucy Reply
fastest finger please
Mean (average) 4... Median (middle term) 3.5.. Mode (frequency) every element in a set has 1 frequrncy
i arrange the data set in ascending order. that is, 1,2,3,4,5,6. then find the data set that falls in the middle. in this case, 3 & 4 fall in the middle. you then sum and obtain the average. that is, (3+4)/2=3.5. therefore, 3.5 is the median.
both of you are correct.
hello guys
great to be here
how does a line graph look
pls who knows how line graph look like
line graph usually have a straight line running through axis
am new here anyone willing to orient me?
find the media of the following numbers 61,64,67,70,73
lucy Reply
my body pls
what happen to your body@hana
what is the percentile for the set of data in the class C and frequency F(c,f)given by (9.3-9.7,2) (9.8-10.2,5) (10.3-10.7,12) (10.8-11.2,17) (11.3-11.7,14) (11.8-12.2,6) (12.3-12.7,3) (12.8-13.2,1)
Chinwendu Reply
how to find median
Hrishe Reply
arrange ascending and desending order than the mid value is Median
what if it is a group data
mean/ medium/ mode
n\2 and n+1\2
An operational manager at a manufacturing company is interested in the level of satisfaction of computer buyers. The manager has developed a satisfaction scale of 1-10 to mark their level of understanding with the company.What is the population of the interest?
thomas Reply
Any clues
how to use grouped and ungrouped data
Hassan Reply
Just a test from gplay
Lucy Reply
how come 5.67
Mano Reply
by dividing 11.37 on 2
by dividing 11.34 on 2
what is index number?
What is the differences between quota an lottery system of sampling
What are the are the characteristics that are critically expedients in selecting the sample size
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
Mikki Reply
solve the question please
can some please help solve so that we learn some
It is a square chi
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
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"
sorry the last f's numbers : "6 and 4" which are the observed values for 5 and 6 (expected values)
can't understand basic of statistics ..
Sorry I see my mistake, we have to calculate the expected values
So we need this equation: P= (X=x)=(n to x) p^x(1-p)^n-x
why it is not possible brother
were n= 2 ( binomial) x= number of makes (0 to 6) and p= probability, could be 0.8.
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
tomorrow I'll post the answer, I'm so tired today, sorry for my mistake in the first messages.
It is possible, sorry for my mistake
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
how to start this book, who is reading thins first time
Nissar Reply
It is my first time reading this book
Good one

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