Question

ation showed that a family of four spends an average of $215.60 per day while on vacation a sample of 64 farmilices of four vacationing at Niagara F A survey conducted by the American Automobile Associ $215.60 per day while on vacation. Suppose a sample of 64 families of four vacationing at Niagara Falls resulted in a sample mean of S252.45 per day and a sample standard deviation of $77.50. a. Develop a 95% confidence interval estimate of the mean amount spent per day by a family of four visiting Niagara Falls (to 2 decimals). b. Based on the confidence interval trom part (a), does it appear that the population mean amount spent per day by families visiting Niagara Falls differs from the mean reported by the American Automobile Association? Select

Answer 1

Answer

(A) Population standard deviation is unknown, so we will use t distribution.

we have

degree of freedom = n-1 = 64-1 = 63

using degree of freedom and alpha level = 1-0.95 = 0.05, in the t distribution table

we get, t value = 2.00

Using the confidence interval formula

setting the given values, we get

this gives us

So, required 95% confidence interval is (233.08,271.83)

(b) Yes, it is clear from the confidence interval that the population mean is outside the lower and upper bound of confidence interval. So, when the population mean is outside confidence interval range, then we say that the population mean amount spent per day by families visiting Niagara falls differs from the mean reported by the American Automobile Association.