Part Il: Calculation 1. Statistical Analysis (Vormal table on the back of Result
ID: 3356062 • Letter: P
Question
Part Il: Calculation 1. Statistical Analysis (Vormal table on the back of Result Summary Page.) a. The sample sizes required for estimating trip production rates in selected zones are to be determined through mail survey. For one residential zone, the sample mean is 300 and sample standard deviation is 60. Assume that an absolute error bound is ±15 is desired for the project, determine the sample size needed to achieve the confidence level of 95%. (5 pts) b. Suppose that 50 samples have been collected after the survey. The sample mean is 320 and the sample standard deviation is 30. At what confidence can one assert that the estimation is within an absolute error bound of 7? How about within a relative error about of 10%? ( 10 pts) c. For the data collection study described in a, assuming the required sample size is 100, the expected response rate will be more than 30%, a $1 incentive is to be sent along with the mail survey to households in this zone. They wi receive the incentive whether or not they respond. Each mail survey costs 50 cents for postage and printing. For those who responded, they can use the enclosed pre-prepaid First-Class envelop (35 cents each) to mail back to the survey center. The USPS will only charge if the envelop is used. Please determine the total budget needed to request for this area. Note that you may receive responses of more than 30%, (3 extra points) Page 3 of 8 Scanned by CamScannerExplanation / Answer
a)
mean = 300
std. dev. = 60
ME = 15
z-value = 1.96
ME = z*sigma/sqrt(n)
n = (1.96*60/15)^2 = 61.47
i.e. sample size should be 61
b)
ME = z*sigma/sqrt(n)
7 = z*30/sqrt(50)
z = 1.65
This value of z corresponds to 90% CI.