During the winter some of the grape vines of a large vineyard die from the cold. It is profitable to harvest the vineyard only if less than ten percent of the grape vines are dead. To test how well the vineyard has survived the winter, a random sample of 1,000 grape vines is selected. Of these 1,000 vines, 80 were found to be dead. (a) If we construct a 90% confidence interval estimate for the proportion (p) of dead grape vines in the vineyard, then this interval includes the value of 10% dead grape vines (p = 0.10). Is this statement true? (Hint. Your answer would be "False") (b) Suppose now that the null hypothesis that the proportion of dead grape vines in the vineyard equals 0.10, is tested at a 5% significance level against the alternative hypothesis that this proportion is lower. Then the outcome of the random sample implies that we should not harvest the vineyard. Is this statement true? (Hint. Your answer would be "False")