Chapter 4: Q 17. (page 227)

iPhones Suppose $1000$ iPhones are produced at a factory today. Management would like to ensure that the phones’ display screens meet their quality
standards before shipping them to retail stores. Since it takes about $10$ minutes to inspect an individual phone’s display screen, managers decide to inspect a sample of $20$ phones from the day’s production.
(a) Explain why it would be difficult for managers to inspect an SRS of $20$ iPhones that are produced today.
(b) An eager employee suggests that it would be easy to inspect the last $20$ iPhones that were produced today. Why isn’t this a good idea?
(c) Another employee recommends inspecting every fiftieth iPhone that is produced. Explain carefully why this sampling method is not an SRS.

Short Answer

Expert verified

$49 t h, 99 t h, . . ., 999 t h$ Part (a) It may be challenging to keep track of $1000$ phone orders.

Part (b) Inspecting the last $20$ iPhones created is not a good sampling for the quality check of the day's manufacturing.

Part (c) The $20$ iPhones sampled will be the $49 t h, 99 t h, . . ., 999 t h$ , and none of the others will be sampled.

Step by step solution

Part (a) Step 1: Given information

Inspecting an SRS of $20$ iPhones from $1000$ iPhones that are produced today is difficult.

Part (a) Step 2: Concept

A simple random sample (SRS) of size n is made up of $n$ people chosen from the population with an equal chance of being the sample that is actually chosen.

Part (a) Step 3: Explanation

Today, the factory produces a thousand iPhones.

Assuming that no phones can be transported until the inspection is completed, checking a random sample of $20$ phones could cause the shipping process to be delayed. Additionally, the phones must be numbered in some fashion in order to create a random sample. It may be challenging to keep track of $1000$ phone orders.

Part (b) Step 1: Explanation

The plan is to inspect the last $20$ iPhones made on that particular day. Bias is virtually always present in convenience sampling. The last $20$ iPhones produced are unlikely to be indicative of all iPhones produced throughout the day. It's likely that the quality of the iPhones manufactured varies amongst $1000$ iPhones created throughout the day. As a result, inspecting the last $20$ iPhones created is not a good sampling for the quality check of the day's manufacturing.

Part (c) Step 1: Explanation

Another colleague proposes inspecting every fifteenth iPhone produced. A simple random sample $(S R S)$ of size n is made up of n people chosen from the population with an equal chance of being the sample that is actually chosen. Inspection of every $49 t h$ iPhone does not build an SRS since each sample of $20$ iPhones has a different chance of getting chosen. The $49 t h, 99 t h, . . ., 999 t h$ iPhones will be sampled, whereas none of the others will be.