Fiona is a manufacturer of barbecue sauce. She wants to determine the proportion of customers who prefer her brand over that of her major competitors. She sampled 100 consumers of barbecue sauce and found that 68 prefer her brand. At the 1% significance level, is there evidence that more than 60% of consumers of barbecue sauce prefer her brand? Find the p-value of the test. If the true proportion of customers who prefer her brand is 70%, what is the probability that Fiona will not detect this change?

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