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Statistical Analysis: Calculating Population Proportion and Confidence Intervals, Exercises of Statistics

University of Minnesota (UMN) - Twin CitiesStatistics

The calculations for determining the population proportion of women who most feared breast cancer based on a sample survey, as well as the confidence intervals for the sample proportion. The document also includes the assumptions made, the sample size and standard error calculations, and the margin of error and t score for the confidence interval.

Typology: Exercises

2014/2015

Uploaded on 11/03/2015

Junaid.Saiyed
Junaid.Saiyed ๐Ÿ‡บ๐Ÿ‡ธ

4

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2 documents

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bg1
Junaid'Saiyed'
STAT'3011'
'
8.21'
a)'
'
'๐‘ ๐‘’ =!(!!!)
!'
'
๐‘'='0.61'
'
๐‘ ๐‘’ =
0.61(1โˆ’0.61)
1000 '
'
='0.015'
'
Sample'Proportion'+/@'1.65'*'se'
'
='0.61'+/@'1.65'*'0.015'
='0.61'+/@'0.025'
='(0.585,'0.635)'='Population'proportion'of'women'who'most'feared'breast'cancer.'
'
b)'
2'Assumptions:'
a) Data'obtained'by'randomization'
b) A'large'enough'sample'size'n'is'obtained'so'that'the'number'of'successes'n๐‘'
and'number'of'failures'n 1โˆ’๐‘'are'both'at'least'15'
'
'
8.51)'
a)'m'='25,'๐œŽ'='200'
'
๐‘›=!
๐œŽ!๐‘ง!
๐‘š!!'
z'='1.96'(based'on'95%'confidence'interval)'
'
='153664/625,'which'is'roughly'246'
'
b)'n'='246,'๐œŽ'='300'
'
๐‘›=!
๐œŽ!๐‘ง!
๐‘š!!'
pf3

Partial preview of the text

Download Statistical Analysis: Calculating Population Proportion and Confidence Intervals and more Exercises Statistics in PDF only on Docsity!

Junaid Saiyed STAT 3011

a)

!(!!!) ! ๐‘ = 0.

Sample Proportion +/-ยญโ€ 1.65 * se = 0.61 +/-ยญโ€ 1.65 * 0. = 0.61 +/-ยญโ€ 0. = (0.585, 0.635) = Population proportion of women who most feared breast cancer. b) 2 Assumptions: a) Data obtained by randomization b) A large enough sample size n is obtained so that the number of successes n๐‘ and number of failures n 1 โˆ’ ๐‘ are both at least 15 8.51) a) m = 25, ๐œŽ = 200 ๐‘› =

z = 1.96 (based on 95% confidence interval) = 153664/625, which is roughly 246 b) n = 246, ๐œŽ = 300 ๐‘› =

๐‘š!^ = 345744/246 = 1405.

  1. 46 = 37.49 = Margin of error 8.78) a) !!!!!!!!! ! = Sample mean = 1. ๐‘  =

Plug in data

!".! ! = 2.074 = Standard Deviation Standard Error: ๐‘ ๐‘’ =

!.!"# !

b) Sample mean +/-ยญโ€ ๐‘ก!.!" * standard error Sample mean = 1. Standard error = 0. Degrees of Freedom = n โ€“ 1 = 5 โ€“ 1 = 4 ๐‘ก!.!" Corresponding to 4 df T score = 2. 1.6 +/-ยญโ€ 2. 775 * 0. = (-ยญโ€0.98, 4.18) = population mean c)

  1. Data obtained by randomization
  2. An approximately normal population distribution 8.87) a)