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# An online clothing retailer knows that historically 20% of potential customers

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An online clothing retailer knows that historically 20% of potential customers that visit its website actually buy something. To see if they can increase the proportion of visitors who buy something, they randomly select 1000 visitors to the website and offer them free shipping if they make a purchase. Of the 1000 visitors who receive this offer, 230 actually buy something. The company wants to test to see if offering free shipping to all customers would increase the proportion who would buy something.

You must do all of your calculations on the TI calculator.

DO NOT Use the Stats -> Tests for any of the problems.

For all hypothesis testing, assume  = 0.05 significance level is given.

Round all answers to three decimal places past the decimal

2. a. Define the parameter and state the hypotheses. [3pts]

b. Find the observed sample statistic and the test statistic. Use proper notation for the sample statistic ( x or p ˆ ), and clearly identify your test statistic as either a z-score or a t-score. [4pts]

c. Find the p-value of your test statistic. You are required to graph the test statistic on its corresponding distribution, shade the appropriate area, and provide correct calculator documentation. Box final answer. [3pts]

d. Make a generic decision about H0 . [2pts]

e. Make a conclusion in the context of the problem. [2pts]

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## [Solved] An online clothing retailer knows that historically 20% of potential customers

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