Statistics_Homework

Q1) 7.2#4




Answers –
Margin of Error= Z a/2 Sqrt(p*(1-p)/n))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=200
Sample Size(n)=500
Sample proportion =0.4
Margin of Error = Z a/2 * ( Sqrt ( (0.4*0.6) /500) )
= 1.96* Sqrt(0.0005)
=0.0429

Q2) 7.2#5




Answers –
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.05 is = 1.96
Sample Proportion = 0.5
ME = 0.06
n = ( 1..06 )^2 * 0.5*0.5
= 266.7778 ~ 267

Q3) 7.2#6




Answers –
Confidence Interval For Proportion

,Answers –
Compute Sample Size ( n ) =(Z a/2 * S.D / ME ) ^2
Zα/2 at 0.1% LOS is = 1.64 ( From Standard Normal Table )
Standard Deviation ( S.D) = 66
ME =5
n = ( 1.64*66/5) ^2
= (108.24/5 ) ^2
= 468.6359 ~ 469

Q5) 7.3 #2




Answers –
Compute Sample Size ( n ) =(Z a/2 * S.D / ME ) ^2
Zα/2 at 0.01% LOS is = 2.58 ( From Standard Normal Table )
Standard Deviation ( S.D) = 2.5
ME =1.2
n = ( 2.58*2.5/1.2) ^2
= (6.45/1.2 ) ^2
= 28.8906 ~ 29


Q5) 9.2 # 7

, Q6) 9.3 # 3




Answers –
Confidence Interval
CI = x1 - x2 ± Z a/2 * Sqrt ( sd1 ^2 / n1 + sd2 ^2 /n2 )
Where,
x1 = Mean of Sample 1, x2 = Mean of sample2
sd1 = SD of Sample 1, sd2 = SD of sample2
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x1)=97.6
Standard deviation( sd1 )=16.2
Sample Size(n1)=302
Mean(x2)=98.8
Standard deviation( sd2 )=13.7
Sample Size(n1)=216
Confidence Interval = [ ( 97.6-98.8) +/- Z a/2 * Sqrt( 262.44/302+187.69/216) ]
= [ (-1.2) - Z a/2 * Sqrt( 1.7379) , (-1.2) + Z a/2* Sqrt( 1.7379) ]
= [ (-1.2) - 1.96 * Sqrt( 1.7379) , (-1.2) + 1.96 * Sqrt( 1.7379) ]
= [-3.79,1.39 ]

Q7) 7.3 # 6




Answers –