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Assignment # 4 (Lessons 31- 36)
Question 1: (Marks: 2+5=7)
a. In a finite population with and , find the mean and variance for the sampling distribution of sample mean for n = 25.
b. The mean and standard deviation of the maximum loads supported by 50 cables are 13 tons and 0.80 tons respectively. Find the 99% confidence interval for the mean of the maximum loads of all cables produced by the company. Also interpret the findings.
Question 2: (Marks: 5+3=8)
Find the
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n=36
s=24
x-bar= 100
82 confidence level
find alpa and z alpha/2
Confidence intervals are used to find a region in which we are 100 * ( 1 - α )% confident the true value of the parameter is in the interval.
For large sample confidence intervals about the mean you have:
xBar ± z * sx / sqrt(n)
where xBar is the sample mean
z is the zscore for having α% of the data in the tails, i.e., P( |Z| > z) = α
sx is the sample standard deviation
n is the sample size
The sample mean xbar = 100
The sample standard deviation sx = 24
The sample size n = 36
The z score for a 0.82 confidence interval is the z score such that 0.09 is in each tail.
z = 1.340755
The confidence interval is:
( xbar - z * sx / sqrt( n ) , xbar + z * sx / sqrt( n ) )
( 94.63698 , 105.3630 )
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