Statistics Assignment | Solutions | Doc

Running head: STATISTICS 1
Statistics
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STATISTICS 2
Solution
Question 1
Solution
Sample size = 10 packages
Average weight of packages =200 grams
Standard deviation =2.5 grams
We need to determine the 92% confidence interval.
The degrees of freedom are given by:
df =10−1=9
The ∝=0.08. For the given alpha value, and 9 degrees if freedom the critical value of t is
tc=1.973. The confidence interval is given by:
CI =( X− tc xs
√n , X + tc xs
√ n )
Therefore
CI =(200− 1.973 x 2.5
√10 , 200+ 1.973 x 2.5
√10 )
lower limit =(200−1.56)=198.44
lower limit =(200+1.56)=201.56
The 92% confidence interval is:
CI =198.44 ≤ X ≤ 201.56

STATISTICS 3
Question 2
Solution
Sample size = 35 packages
Average weight of packages =454 grams
Standard deviation =20 grams
We need to determine the 98% confidence interval.
The degrees of freedom are given by:
df =35−1=34
The ∝=0.02. For the given alpha value, and 34 degrees of freedom the critical value of t is
tc=2.441 The confidence interval is given by:
CI =( X− tc xs
√n , X + tc xs
√ n )
Therefore
CI =
(454−2.441 x 2 0
√35 , 454+ 2.441 x 20
√35 )
lower limit =(454−8.253 ,)=445.747
lower limit =( 454+8.253)=462.253
The 98% confidence interval is:
CI =445.747 ≤ X ≤ 462.253