[4](21) A survey conducted by the American Automobile Association showed that a family of four spends an average of $215.60 per day while on vacation. Suppose a sample of 81 families of four vacationing at Niagara Falls resulted in a sample mean of $252.45 per day and a sample standard deviation of $74.50. We shall use a 0.02 significance level to test the claim that a family of four will spend more money, on average, when vacationing at Niagara Falls per day than the average amount for a family of four claimed by the American Automobile Association. a) Set up the null and alternative hypotheses. Ho: b) Is the test two-tailed, left-tailed, or right-tailed? Explain why. () What is the sampling distribution of the sample statistic? d) What is the value of the test statistic? e) Perform the hypothesis test with a significance level of 2% using the critical value (traditional) method. () What does the p-value mean to the problem situation? @) Based on results of the hypothesis test in part (e)-(f), does it appear that the population mean amount spent per day by families visiting Niagara Falls is more than the mean amount per day for a family of four reported by the American Automobile Association? Explain