Question

Accuracy of price scanners at Walmart. Refer to Exercise 6.129 (p. 377) and the study of the accuracy of checkout scanners at Walmart stores in California. Recall that the National Institute for Standards and Technology (NIST) mandates that for every 100 items scanned through the electronic checkout scanner at a retail store, no more than two should have an inaccurate price. A study of random items purchased at California Walmart stores found that 8.3% had the wrong price (Tampa Tribune, Nov. 22, 2005). Assume that the study included 1,000 randomly selected items.

a. Identify the population parameter of interest in the study.

b. Set up H0 and Ha for a test to determine if the true proportion of items scanned at California Walmart stores exceeds the 2% NIST standard.

c. Find the test statistic and rejection region (at $\mathit{a}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{05}$ ) for the test.

d. Give a practical interpretation of the test.

e. What conditions are required for the inference, part d, to be valid? Are these conditions met?

Short answer

a. The population parameter of interest in the study is the population proportion.

b. The null and alternative hypotheses for the claim are: $H_0:p=0.02$ Against $H_a:p>0.02$.

c. The value of the test statistic is $z=14.32$. The rejection region is $z>1.65$.

d. There is sufficient evidence that the true proportion of items scanned at California Walmart stores exceeds the 2% NIST standard.

e. Since both the values are more than 15, the conditions are satisfied.

Step-by-step solution

Given Information

The sample proportion of items purchased at California Walmart stores is 0.083.

The sample size is 100.

Concept

The conditions required to use one proportion z-test are:

$np=\ge andn(1-p)\ge 15$

Verifying the condition required

e.

Here,

$$\begin{gathered} np=1000\times 0.02 \\ =20 \\ >15 \end{gathered}$$

Also,

$$\begin{gathered} n(1-p)=1000\times 0.98 \\ =980 \\ >15 \end{gathered}$$

Since both the values are more than 15, the conditions are satisfied.