jm00120
05.12.2019 •
Mathematics
Of the 500 sample households in the previous exercise, 7 had three or more large-screen tvs. (a) the percentage of households in the town with three or more largescreen tvs is estimated as ; this estimate is likely to be off by or so. (b) if possible, find a 95%-confidence interval for the percentage of all 25,000 households with three or more large-screen tvs. if this is not possible, explain why not.
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Ответ:
a) The percentage of households in the town with three or more largescreen TVs is estimated as :
The best estimation for the population proportion is :
And that represent the 1.4%.
b) And the 95% confidence interval would be given (0.00370;0.0243).
And the % would be between 0.37% and 2.43%.
Step-by-step explanation:
Data given and notation
n=500 represent the random sample taken
X=7 represent the households with three or more large-screen TVs
estimated proportion of households with three or more large-screen TVs
represent the significance level (no given, but is assumed)
z would represent the statistic (variable of interest)
p= population proportion of households with three or more large-screen TVs
Part a
The percentage of households in the town with three or more largescreen TVs is estimated as :
The best estimation for the population proportion is :
And that represent the 1.4%.
Part b
Yes is possible. We hav that and so we have the assumption of normality to find the interval.
The confidence interval would be given by this formula
For the 95% confidence interval the value of and , with that value we can find the quantile required for the interval in the normal standard distribution.
And replacing into the confidence interval formula we got:
And the 95% confidence interval would be given (0.00370;0.0243).
And the % would be between 0.37% and 2.43%.
Ответ:
c
Step-by-step explanation:
I just know