Chapter 4.1, Problem 16E

(a)

To determine

To explain why it would be difficult for managers to inspect an SRS of $20$ iPhones that are produced today.

Explanation of Solution

Out of $1000$ iPhones produced if a random sample of size $20$ is drawn then the sample size $20$ is quite less compared to total production of the day. In an SRS of $20$ sample out of $1000$ units each of $20$ units has probability,

  $\frac{1}{1000}=0.001$ of being selected , which is very less.

(b)

To determine

To explain why the idea given in the question is not good.

Explanation of Solution

If the last $20$ phones produced are inspected then this sample is not a representative of the total production.

Because there may be a change in the production process (may be machine is not working efficiently) in the end of the day. Any change in the production process influences the quality specification of a certain numbers of successively produced iPhones .The manager wants to ensure that all $1000$ iPhones produced meet the quality specification of the display screen. So, inspecting the last $20$ phones produced does not ensure whether the whole day's production meet the quality specification.

(c)

To determine

To explain why this sampling method is not an SRS.

Explanation of Solution

SRS is a probability sampling in which every member of the population has Equal probability of being included in the sample.

Systematic sampling is partly probabilistic and partly non probabilistic sampling. This sampling method is probabilistic since the first member of the sample is selected at random from first $50$ units(each of first $50$ population units has Equal chance of being selected as first sample unit). This method is non-probabilistic since the other units in the sample are fixed(every fiftieth member is selected after the first unit is selected) by the choice of the first unit.

So, systematic random sampling is not an SRS.