Use the given data to construct a confidence interval for the population standar

Question

Use the given data to construct a confidence interval for the population standard deviation, . Assume that the population has a normal distribution: The football coach randomly selected the following players and timed how long each player took to perform a certain drill. The times (in minutes) were:

[10,10,15,10,11,7,5,5]

Find a 95.0 confidence interval for the population standard deviation

A) 2.6194049<<6.43192582.6194049<<6.4319258

B) 2.2194049<<6.83192582.2194049<<6.8319258

C) 2.6194049<<7.43192582.6194049<<7.4319258

D) None of These

Explanation / Answer

right choice is B) 2.2194049<<6.8319258

95% confidence interval for ={ sqrt((n-1)s2/chi-sq( alpha/2 ,n-1)),sqrt((n-1)s2/chi-sq(1- alpha/2 ,n-1)) }

={sqrt((8-1)*3.36*3.36/16.01),sqrt((8-1)*3.36*3.36/1.69)}={2.22, 6.84}

chi-sq(1-0.05/2,7)=1.69,                   chi-sq(0.05/2,7)=16.01

nearest choice is B) 2.2194049<<6.8319258

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