Inference in Population Variance
BUS 173
Assignment 2
Prepared For:
Md. Siddique Hossain
(Sqh)
Answer to the question no 01
Inference Regarding the population variance, σ 2
An important area of statistic is concern with making inference about the population variance. Knowledge of population variability is an important element of statistical analysis. Two possibilities arise For example.
A) For a car rental agency . * Tires with low variability’s is preferred compared with durable lives with high variability.
B) A bank policy favor a single waiting line that feeds into several tellers. * may remain same whether more than one lines formal. * σ 2 may be lower in single line. * σ 2 is higher in more than one line.
Like the population mean µ , σ 2 is ordinarily unknown, and its value must estimated using sample data.
Sample variance
A random sample of n observations drawn from a population with unknown mean and unknown varience σ 2 .Denote the sample x 1, x2 ,…….xn
The population variance is the expectation σ 2 = E [ ( x - µ) ] , Which sagely that we consider the mean of ( xi – ) and n observation Since µ is unknown the sample mean is used to compute a sample variance.
The quantity
S2= 1/n-1i=1n (xi-) is called a sample variance ,and its square root s is called the sample standard deviation .
Given a specific random sample variance and the sample variance would be different for each random sample.
P ( x2n-1 , 1-α/2 ≤ x2n-1 ≤ x2n-1 ,α/2) n= 25 , n-1=24
P (x2n-1 < 12.40) =0.025 ,P (x2n-1 > 12.40)= 0.975,P(x2n-1 > 39.36) = 0.025,P (x2n-1 < 39.36) = 0.975 Chapter 09 Hypothesis
Chi-squared distribution
For a large sample size the sampling distribution of chi square can be closely approximated by a continuous curve known as the chi-squared distribution. If we can assume that a population distribution is normal, then it can be
Assignment 2
Prepared For:
Md. Siddique Hossain
(Sqh)
Answer to the question no 01
Inference Regarding the population variance, σ 2
An important area of statistic is concern with making inference about the population variance. Knowledge of population variability is an important element of statistical analysis. Two possibilities arise For example.
A) For a car rental agency . * Tires with low variability’s is preferred compared with durable lives with high variability.
B) A bank policy favor a single waiting line that feeds into several tellers. * may remain same whether more than one lines formal. * σ 2 may be lower in single line. * σ 2 is higher in more than one line.
Like the population mean µ , σ 2 is ordinarily unknown, and its value must estimated using sample data.
Sample variance
A random sample of n observations drawn from a population with unknown mean and unknown varience σ 2 .Denote the sample x 1, x2 ,…….xn
The population variance is the expectation σ 2 = E [ ( x - µ) ] , Which sagely that we consider the mean of ( xi – ) and n observation Since µ is unknown the sample mean is used to compute a sample variance.
The quantity
S2= 1/n-1i=1n (xi-) is called a sample variance ,and its square root s is called the sample standard deviation .
Given a specific random sample variance and the sample variance would be different for each random sample.
P ( x2n-1 , 1-α/2 ≤ x2n-1 ≤ x2n-1 ,α/2) n= 25 , n-1=24
P (x2n-1 < 12.40) =0.025 ,P (x2n-1 > 12.40)= 0.975,P(x2n-1 > 39.36) = 0.025,P (x2n-1 < 39.36) = 0.975 Chapter 09 Hypothesis
Chi-squared distribution
For a large sample size the sampling distribution of chi square can be closely approximated by a continuous curve known as the chi-squared distribution. If we can assume that a population distribution is normal, then it can be