Problem 12 - Basic Statistics for Business and Economics with Student

Question

AVX Stereo Equipment, Inc., recently began a "no-hassles" return policy. A sample of 500 customers who had recently returned items showed 400 thought the policy was fair, 32 thought it took too long to complete the transaction, and the rest had no opinion. On the basis of this information, make an inference about customer reaction to the new policy.

Step-by-Step Solution

Answer

80% of customers think the policy is fair, indicating it is well-received overall.

Step 1: Understand the Given Information

We have a sample of 500 customers who have interacted with a new return policy. In this sample, 400 customers thought the policy was fair, 32 thought it took too long, and the rest had no opinion.

Step 2: Calculate Those With No Opinion

We need to calculate how many customers had no opinion. The total number of customers is 500. If 400 found it fair and 32 thought it took too long, we subtract those from 500 to find the remainder: \[500 - 400 - 32 = 68\].Therefore, 68 customers had no opinion.

Step 3: Determine the Proportion of Customer Opinions

Calculate the proportion of each group among the 500 customers sample: 1. Fair: \(\frac{400}{500} = 0.8\) or 80%.2. Took too long: \(\frac{32}{500} = 0.064\) or 6.4%.3. No opinion: \(\frac{68}{500} = 0.136\) or 13.6%.

Step 4: Make an Inference About Customer Reaction

Since 80% of the customers found the new policy fair, this suggests the policy is generally well-received. Only a small percentage (6.4%) found the process took too long, and 13.6% had no opinion. This indicates strong support among those who have an opinion.

Key Concepts

Customer Satisfaction Survey

Conducting a customer satisfaction survey is a great way to gather important feedback from consumers. It provides valuable information about their experiences and perceptions.
These surveys help companies to assess how well they are meeting customer expectations and where they can improve.
In a customer satisfaction survey, participants are usually asked to respond to questions about their experience with a product or service. A survey can include aspects like usability, customer service, or specific features.

Here are some common areas these surveys might evaluate:

• Overall satisfaction with the product or service.
• Likelihood to recommend the product or service to friends or family.
• Quality and efficiency of customer service during interactions.

Analyzing this feedback assists companies in understanding customer needs and aligning their strategies toward fulfilling them.

Proportions

Proportions are a statistical concept used to describe how a part relates to a whole. In simpler terms, it is how we express the fraction of the total that a particular subset represents.
For instance, if we want to understand how customers feel about a new return policy, proportions can clearly show how sentiments are spread among the customers surveyed.

These steps help in calculating proportions:

• Identify the total number of respondents. For example, in the given survey, there are 500 customers.
• Determine how many respondents fall into each category. In our case, 400 found the policy fair, 32 thought it was lengthy, and 68 had no opinion.
• Divide the number in each category by the total number of respondents to find the proportion. For the customers who found the policy fair:

The proportion formula is: \[\text{Proportion} = \frac{\text{Number in category}}{\text{Total number of respondents}}\]Applying this formula helps us interpret how widespread each opinion is among the total surveyed.

Sample Analysis

Analyzing a sample involves examining a subset of a larger population to draw conclusions about the entire group. This method is often used when it's impractical to survey everyone.
In the provided example, a sample of 500 customers gives us insights into general customer reactions to a return policy.

When conducting a sample analysis, consider the following steps:

• Ensure that the sample accurately represents the entire population. A good sample should mirror the diversity and characteristics of the total customer base.
• Use statistical methods to summarize the data, such as computing proportions or means.
• Interpret the findings thoughtfully. For instance, in our scenario, since 80% of customers find the policy fair, the analysis suggests widespread approval.

Effective sample analysis helps businesses make informed decisions based on customer feedback, leading to better customer satisfaction and retention.