# Qnt 571 Week 2

Ch 8.   #21. Sampling error is the amount of error in sampling a portion of the population, instead of the entire population.   Sampling error can be reduced by sampling a large amount of the population, and using a random sample or stratified sample of populations.   If the sampling error is ‘0’, this theoretically means that the sample represented an accurate portion of the population, or by sampling the entire population.
Ch. 8 #22 The reasons for sampling include: saving time and not having to observe/contact the entire population; sampling all items in the population may be prohibitive; physically impossible to question the entire population, some tests may be destructive; proportion of samples make the results adequate.
Ch 8. #34.
A. St. Dev divided by the square root of the sample   = 40,000/square root of 50.0   = 5656.8
B.   The expected shape will be a bell curve
C.   P (X-u) / (o) >   112000 – 110000/40,000   =   P (z > 0.05)
1 – 0.5199         = 0.4801
D.   Sample mean of more than 100,000 but less than 112,000?
= P (100000 < X < 112,000)
= P (100000-110000/40000   < X – u/o < 112000 -110000/40000)
= 0.5199 – 0.4013
= 0.1186

Ch. 9 #32
a. Estimated population mean would be 3.01 lbs
b. Confidence interval =   invT (0.975, 35) * 0.03/square root of 36 = 0.0102
CI of 95% = 3.01 - .0102 < u < 3.01 + .0102
#34
a. mean – z*stdev/squart root (N)   to mean+ z *stdev/square root of N
z = 1.96   N = 50   stdev = 6.2   mean = 26
26 – 1.96*6.2/squart root (50) to 26 + 1.96*6.2/square root (50)
= 24.28 to 27.72
having 28 weeks as the mean would not be likely because it is outside the 95% confidence interval.   The mean should be within 24 weeks to 27 weeks.

#46.     14/220 =0.64 sample proportion
14/220 – 2.5758 * sq (14/220)*1-14/220)/220) to 12/220 + 2.5758 * sqrt(14/220) * ( 1-14/220)/220)     = 0.0212 to 0.1060
B.   10% is within the confidence interval, and it is reasonable.

Second half
14/400 - 2.5758*sqrt(14/400*(1-14/400)/400) to...