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 Walmart stores in California was conducted. At each of 60 randomly selected Walmart 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 Walmart 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 Walmart spokesperson claims that 99% of California Walmart 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 Walmart stores that must be sampled in order to estimate the true proportion to within .05 with 90% confidence using the large-sample method.