Question

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 64 families of four vacationing at Niagara Falls resulted in a sample mean of $252.45 per day and a sample standard deviation of $78.50.

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 from 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? Yes or No

Answer 1

a)

From T table,

t critical value at 0.05 level with 63 df = 1.998

95% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

252.45 - 1.998 * 78.50 / sqrt( 64) < < 252.45 + 1.998 * 78.50 / sqrt( 64)

232.84 < < 272.06

95% CI is ( 232.84 , 272.06 )

b)

Since claimed mean 215.60 falls outside the confidence interval, we have sufficient evidence to support

the claim that the population mean amount spent per day by families visiting Niagara Falls differs from

the mean reported by the American Automobile Association.

Yes.