The 2016 World Series was the 112th edition of Major League Baseball\'s champion
ID: 3232357 • Letter: T
Question
The 2016 World Series was the 112th edition of Major League Baseball's championship series, a best -of-seven playoff between the National League champion Chicago Cubs and the American League champion Cleveland Indians. The Cubs defeated the Indians in seven games, for their first World Series victory in 108 years. The following table has some details about the games. (Data from https://en.wikipedia.org/wiki/2016 World Series) Report the following summary statistics for the Attendance at the 2016 World Series, rounded to the nearest tenth. 1. Mean: ___ Median: ___ Population Standard Deviation: ___ Range: ___ ii. Let's now treat the 2016 World Series as a sample of attendance at World Series games. Use the given data to compute a 90% confidence interval estimate of World Series attendance. Report confidence interval limits to one decimal. iii. Use a complete sentence to interpret the meaning of this interval, in context.Explanation / Answer
follwoing information has been generated
(i) mean=sum/n=39657.57
(ii) median=middle observation{((n+1)/2 )=(7+1)/2=4th observation) }=38172
median is middle observation after data is arranged in ascending or descending order. here data is arranged in ascending order
population standard deviation=sqrt(sum(x-mean)2/n)=sqrt(22047502/7)=1774.72
range=largest - lowest=41711-38091=3620
(ii) (1-alpha)*100% confidence interval for mean=mean± z(alpha/2)*sd/sqrt(n)
90% confidence interval for mean=39657.57±z(0.1/2)*1774.72/sqrt(7)=
=39657.57±1.645*1774.72/sqrt(7)=39657.57±1103.43=(38554.14,40761.00)
(iii) To interpret a confidence interval remember that the sample information is random - but there is a pattern to its behavior if we look at all possible samples. Each possible sample gives us a different sample proportion and a different interval. But, even though the results vary from sample-to-sample, we are "confident" because the margin-of-error would be satisfied for 90% of all samples .
S.N. attendence(x) (x-mean) (x-mean)2 1 38091 -1566.57 2454146 7 38104 -1553.57 2413584 6 38116 -1541.57 2376442 2 38172 -1485.57 2206922 3 41703 2045.429 4183778 4 41706 2048.429 4196060 5 41711 2053.429 4216569 sum= 277603 7.28E-12 22047502 n= 7 mean= sum/n=277603/7= 39657.57Related Questions
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