Persons aged 55 and over represented 21.3% of the U.S. population in the year 2000. This group is expected to increase to 30.5% by 2025. In terms of actual numbers of people, the increase is from 58.6 million to 101.4 million. Restaurateurs have found this market to be important and would like to make their businesses attractive to older customers. One study used a questionnaire to collect data from people aged 50 and over. For one part of the analysis, individuals were classified into two age groups: 50 to 64 and 65 to 79. There were 267 people in the first group and 263 in the second group. One set of items concerned ambience, menu design, and service. A series of statements were rated on a 1 to 5 scale with 1 representing "strongly disagree" and 5 representing "strongly agree". The data are located in the file called "restaurant" on the J:drive.
Statement 50-64 65-79
"Most restaurants are too dark" 2.75 /2.93
"Most restaurants are too noisy" 3.33/ 3.43
"Background music is often too loud" 3.27/ 3.55
"Restaurants are too smoky" 3.17/ 3.12
"Tables are too small" 3 /3.19
"Tables are too close together" 3.79/ 3.81
"Print size is not large enough on menu" 3.68/ 3.77
"Glare on menu makes it difficult to read" 2.81 /3.01
"Colors of menus make them difficult to read" 2.53 /2.72
"It is difficult to hear the service staff" 2.65/ 3
"I would rather be served than serve myself" 4.23 /4.14
"I wuld rather pay the server than the cashier" 3.88/ 3.48
"Service is too slow" 3.13 /3.1
Question #1: For each statement compute the z statistics and the associated P-value for the comparisons between the two groups. For these calculations you can assume that the standard deviation of the difference is .08, so z is simply the difference in means