The steps I would take to tackle this task would be as follows.$$

$1.$ Defining the Problem and Objective

$-$ Objective: Estimate the average price customers are willing to pay for a T$-$Shirt in the new brand

$-$ Goal: Help Walmart make an informed decision about pricing to ensure it's competitive and also profitable.

$2.$ Data Collection$$

$-$ Survey Customers: Create a survey or tool for market research to ask customers about price expectations for a new brand of T$-$Shirts.

$-$ Competitive Analysis: Look at pricing of other similar brands in the market, and identify the range that customers are wiling to pay.$$

$-$ Demographics: Identify demographics from your population sample to better understand your target market and their spending habits.$$

$3.$ Sampling Method

$-$ Random Sampling: to ensure data is representative random sampling is the best method to avoid vias in choosing customers and will ensure that the survey data reflects the preferences of a general customer base.$$

$-$Sample Size: Ensure that the sample size is large enough to make estimates reliable and provide most accurate results.$$

$4.$ Data Analysis$$

$-$ Calculating the mean: The most straight forward way to identify the average amount customers are willing to pay is by calculating the mean.

$-$Consider Variability: Taking the spread of data into account is also a crucial step to understand what the customer base is interested in paying. Standard Deviation would be the method used for this.$$

$-$Confidence Interval: If you want to express a range where a true average falls you can use this method. It will give a range of prices$95\%$ of customers are willing to pay for example between $$12-$$$18.$ This is achieved by establishing an upper and lower bound range in a set of data.$$

$5.$ Interpreting Results to Manager

Presenting the results in an easy to digest and visual way is important to ensure that your manager is receptive to the data gathered. Firstly begin by explain the overall average that customers are willing to pay, and then explain the confidence interval. Use competitive data to bring context to the customer survey data and the market as a whole. Finally suggest that the price be within range found in the confidence interval and use sales data to adjust price based on outcome.$$