Silvestro
Section Joe 003
Statistics 101, Homework 7
Chapter 13
22) Population = 9,000+ readers of the magazine
Parameter of Interest = Rating of products within magazine
Sampling Frame = Readers of magazine
Sampling Size = 225 readers
Sampling Design = Simple random sampling of population
Sources of Biases or other problems = Sample size represents less than 2.5% of all readers.
Since the sample represents such a small portion of the population the results may not be
representative of the entire population.
28a) This represents a voluntary response strategy. The voluntary response bias which exists
in all voluntary response surveys creates a strong bias in this data, since people with very strong
opinions are more likely to respond, as are people with more negative opinions.
b) This represents cluster sampling. The bias which may exist in this case is that only the
people who choose to attend the meeting have their opinions recorded, leaving the survey biased
towards the opinions of those people more likely to attend the meeting.
c) This represents cluster sampling. The bias which could exist in this case is that the results of
the survey may only reflect the opinions of people who happened to be in a particular geographic
area on a given day. As a result, the survey will not fully reflect the beliefs of the entire
employee population.
d) This represents systematic sampling. The bias which could exist in this case is that the
customers could be recorded in a particular pattern, making the each hundredth person biased
towards a particular result.
32) The company cannot determine the proportion of all customers at this dealership who
believe that their service is extremely good based upon this survey. This is because that 55%
of customers felt this way when surveyed represents a sample statistic, rather than a population
parameters (which would include the mean and variation of all responses). The results of a
survey of a sample cannot be applied to a population at large because reality is not reflected by
the surveying of a sample. The 55% sample statistic can only be to used help estimate the
proportion of people at this dealership who are extremely satisfied.
Nothing can be inferred about other dealerships, but the results at this dealership can be
compared to identical surveys at other dealerships to determine if tampering has occurred.
Chapter 14
26a) Mean = 1,020 g SD = 8 g 1,000 = 20 / 8 = 2.5 SDs from mean
Chance of falling more than 2.5 SDs below mean = 6.21% according to normal tables
Type I error rate = 6.21%
b) Type II error rate = Chance that no action is taken to correct a problem
Probability that this occurs = 1 P(Type I error) = 93.8%
28a) The company could establish a durability test which will measure quality, specifically
testing the durability of the ink on the products. Only a sample of photos needs to be tested each
time the process is undertaken, so that a mean quality can be established. Once that is done then
the process can be halted only when the mean of a sample falls far enough away from the mean
quality to warrant a change.
b) The company should group the photos into a large batch to increase sample size so that it is
more than 10 times the size of the measured skewness and absolute value of the kurtosis, which
is a prerequisite for normal distribution to be used. By making n larger the company can help
shrink both Type I and Type II error rates.
30) Control Limits for x-bar chart = (mean) (+/-) ((SD) / (square root of n))
a) Mean = 100, SD = 20, n = 25
100 + 20 / (square root of 25) = 104 = Upper control limit
100 20 / (square root of 25) = 96 = Lower control limit
Lower control limit = 96
Upper control limit = 104
b) Mean = 2000, SD = 2000, n = 100
2000 + 2000 / (square root of 100) = 2200 = Upper control limit
2000 2000 / (square root of 100) = 1800 = Lower control limit
Lower control limit = 1800
Upper control limit = 2200
32a) Control limit = (+/-) 3
Probability that one sample falls outside of 3 = 2.7%
Probability of (A u B u C u D) = P(A) + P(B)
2.7% x 10 samples = 27% chance that at least one falls beyond limit
There is a 27% chance that at least one sample falls beyond the control limit.