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iPhones Suppose 1000 iPhones are produced at a factory today. Management would like to ensure that the phones鈥 display screens meet their quality

standards before shipping them to retail stores. Since it takes about 10 minutes to inspect an individual phone鈥檚 display screen, managers decide to inspect a sample of 20 phones from the day鈥檚 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鈥檛 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

49th,99th,...,999thPart (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 49th,99th,...,999th, and none of the others will be sampled.

Step by step solution

01

Part (a) Step 1: Given information

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

02

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.

03

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.

04

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.

05

Part (c) Step 1: Explanation

Another colleague proposes inspecting every fifteenth iPhone produced. 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. Inspection of every 49th iPhone does not build an SRS since each sample of 20iPhones has a different chance of getting chosen. The49th,99th,...,999th iPhones will be sampled, whereas none of the others will be.

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