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 2 should have an inaccurate price. A study of the accuracy of checkout scanners at Wal-Mart stores in California was conducted. At each of 60 randomly selected Wal-Mart stores, 100 random items were scanned. The researchers found that 52 of the 60 stores had more than 2 items that were inaccurately priced.
a. Give an estimate of p, the proportion of Wal-Mart stores in California that have more than 2 inaccurately priced items per 100 items scanned.
b. Construct a 95% confidence interval for p.
c. Give a practical interpretation of the interval, part b.
d. Suppose a Wal-Mart spokesperson claims that 99% of California Wal-Mart stores are in compliance with the NIST mandate on accuracy of price scanners. Comment on the believability of this claim.
e. Are the conditions required for a valid large-sample confidence interval for p satisfied in this application? If not, comment on the validity of the inference in part d.
f. Determine the number of Wal-Mart stores that must be sampled in order to estimate the true proportion to within .05 with 90% confidence using the large-sample method.