Please.. RESOLVE THE FOLLOWING EXERCISES. THE COMPUTES CARRIED OUT IN EACH STEP
ID: 3046000 • Letter: P
Question
Please.. RESOLVE THE FOLLOWING EXERCISES. THE COMPUTES CARRIED OUT IN EACH STEP MUST BE DISPLAYED IN EACH ONE. Thanks In anticipation, really need some help.
1. ESTIMATION OF INTERVAL FOR THE PROPORTION OF A POPULATION:
The manager of a bank wants to determine the proportion of clients who are paid for the funds in the checking accounts.
A random sample of 100 clients was selected from the 30 of them earning interest in their accounts.
a. Estimate the proportion of customers who are paid interest in their accounts at 90% confidence.
2. ESTIMATION OF INTERVAL OF THE POPULATION AVERAGE WITH POPULATION STANDARD DEVIATION KNOWN:
A car parts wholesaler needs an estimate of the average life of the "windshield wipers". Management has determined that the standard deviation
population is 6 months. In a simple random sample of 100 the average duration of 21 months. A confidence level of 95% establish
an estimate of the average life of the "windscreen wipers".
3. ESTIMATION OF INTERVAL OF THE POPULATION AVERAGE WITH DEVIATION STANDARD POPULATION UNKNOWN:
A firm is considering moving its operations from the city to the suburbs. One factor to consider is the time it will take employees
arrive to work. In a survey of 20 employees the average time of 36.5 minutes with standard deviation of 11.3 minutes. On a level
Confidence of 99% establish an estimate of the time it will take for employees to get to work.
Explanation / Answer
(1) here proportion p=x/n=30/100=0.3
SE(p)=sqrt(p(1-p)/n)=sqrt(0.3*(1-0.3)/100)=0.0458
(1-alpha)*100% confidence interval for population proportion (P)=sample proportion (p) ±z(alpha/2)*SE(p)
90% confidence interval for P=p±z(0.1/2)*SE(p)=0.3±1.645*0.0458=0.3±0.0753=(0.2247,0.3753)
(2)
(1-alpha)*100% confidence interval for population mean=sample mean±z(alpha/2)*sd/sqrt(n)
95% confidence interval for population mean=sample mean±z(0.05/2)*sd/sqrt(n)
(3)
(1-alpha)*100% confidence interval for population mean=sample mean±t(alpha/2,n-1)*sd/sqrt(n)
99% confidence interval for population mean=mean±t(0.01/2, n-1)*sd/sqrt(n)
n= 100 sample mean= 21 sd= 6.00 z-value lower limit upper limit 95% confidence interval 1.96 19.82 22.18