How accurate are price scanners? Recent customer complaints about items being scanned for prices higher than listed, or mis-scans. This has prompted a large, national grocery chain to audit its newly installed price scanners at one of its stores. Industry standards account for 2 % of items to be mis-scanned. The statistical hypotheses to be tested is
H0 : p = 0.02 HA : p > 0.02
(a) Statistical testing is to be carried out at α = 0.05. The grocery chain is to randomly pick, scan, and compute the proportion of n = 500 items that are mis-scanned.
What value of this sample proportion will indicate that more than 2 % of the time items at this grocery store are mis-scanned? Find the value of ̂p_Critical.
̂p_Critical = (use at least four decimals in your answer)
(b) Of the n = 500 items scanned, 18 were mis-scanned. Consider the decision to be made about H0 from this data. What type of error would be made here?
A. Type I error
B. A correct decision
C. Type II error
(c) Find the P-value, and interpret its meaning in the context of these data.
If the proportion of mis-scanned items is equal to 2%, the probability of observing stronger evidence against H0 is (use at least four decimals in your answer).
(d) Complete the sentence below to correctly explain a Type I error in the context of these data.
These data would indicate that the proportion of items mis-scanned at this particular store is greater than 2%, when the proportion of items mis-scanned at this store is actually equal to 2%.
(e) If the proportion of all items mis-scanned at this particular store is 2.8% (p = 0.028), find the probability of concluding that the proportion of all items mis-scanned is more than 2%.
β = (use at least four decimals in your answer)