Airline travelers often choose which airport to fly from based on flight cost. Cost data (in dollars) for a sample of flights to eight cities from Dayton, Ohio, and Louisville, Kentucky, were collected to help determine which of the two airports was more costly to fly from. A researcher argued that it is significantly more costly, on the average, to fly out of Dayton than Louisville. The data, in dollars, are shown in the accompanying table:

Airline travelers often choose which airport to fly from based on flight cost. Cost data (in dollars) for a sample of flights to eight cities from Dayton, Ohio, and Louisville, Kentucky, were collected to help determine which of the two airports was more costly to fly from. A researcher argued that it is significantly more costly, on the average, to fly out of Dayton than Louisville. The data, in dollars, are shown in the accompanying table: Destination Dayton Louisville Chicago-O-Hare $319 $142 Grand Rapids, Michigan 192 213 Portland, Oregon 503 317 Atlanta 256 387 Seattle 339 317 South Bend, Indiana 379 167 Miami 268 273 Dallas-Ft. Worth 288 274 a). At 5% level of significance, is there sufficient evidence to support the researcher's argument? Your conclusion must be in terms of the P-Value. Show all necessary work. b). What type of error is possible and describe this error in terms of the problem. c). Construct a 95% confidence interval for the difference in the actual average cost of flying between the two airports. Using this interval estimation, is there sufficient evidence support the researcher's argument? Explain Carefully. d). Interpret this interval estimation. e). Explain the sampling design in this problem. Can you propose another type of sampling design (if any) that could be used to perform the analysis of parts (a) and (c)? Give one advantage and one disadvantage of the design you are proposing. Explain carefully