Q. 65 - The Practice of Statistics for AP

Question

Paying high prices? A retailer entered into an exclusive agreement with a supplier who guaranteed to provide all products at competitive prices. The retailer eventually began to purchase supplies from other vendors who offered better prices. The original supplier filed a lawsuit claiming violation of the agreement. In defense, the retailer had an audit performed on a random sample of $25$ invoices. For each audited invoice, all purchases made from other suppliers were examined and compared with those offered by the original supplier. The percent of purchases on each invoice for which an alternative supplier offered a lower price than the original supplier was recorded.$26$ For example, a data value of $38$ means that the price would be lower with a different supplier for $38\%$ of the items on the invoice. A histogram and some computer output

for these data are shown below. Explain why we should not carry out a one-sample t-test in this setting.

Step-by-Step Solution

Answer

Random: $25$ invoices are randomly sampled. $10\%$ rule is less than large counts.

Step 1: Given information

The original supplier filed a lawsuit claiming a violation of the agreement. 

In defense, the retailer had an audit performed on a random sample of $25$ invoices. The percent of purchases on each invoice for which an alternative supplier offered a lower price than the original supplier was recorded at $26$.

For example, a data value of $38$ means that the price would be lower with a different supplier for $38\%$of the items on the invoice.  

Step 2: Explanation

The percent of purchases on each invoice for which an alternative supplier offered a lower price than the original supplier was recorded $26$. The one-sample t-test is a member of the t-test family.  

All the tests in the t-test family compare differences in mean scores of continuous-level (interval or ratio), normally distributed data.  Unlike the independent or dependent-sample t-tests, the one-sample t-test works with only one mean score.  The one-sample t-test compares the mean of a single sample to a predetermined value to determine if the sample mean is significantly greater or less than that value. 

For this case, Random: $25$ invoices are randomly sampled. $10\%$rule is less than large counts.