Older customers in restaurants. Persons aged 55 and over represented 21.3% of th
ID: 3020058 • Letter: O
Question
Older customers in restaurants. 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. Restauranteurs 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.19 For one part of the analysis, individuals were classified into two age groups: 50–64 and 65–79. There were 267 people in the first group and 263 in the second. 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.” In some cases the wording of questions has been shortened in the table below. Here are the means:
Item
50-64
65-79
Ambience:
Most restaurants to dark
2.75
2.93
Most restaurants to noisy
3.33
3.43
Background music often to loud
3.27
3.55
Restaurants are to smoky
3.17
3.12
Tables are too small
3.00
3.19
Tables are too close together
3.79
3.81
Menu design:
Print size not large enough
3.68
3.77
Glare makes menu hard to read
2.81
3.01
Color of menu make hard to read
2.53
2.72
Service:
It is hard to hear the service staff
2.65
3.00
I would rather be served
4.23
4.14
I would rather pay server
3.88
3.48
Service is too slow
3.13
3.10
First examine the means of the people who are 50 to 64. Order the statements according to the means and describe the results. Then do the same for the older group. For each statement compute the older Z statistic and the associated P-value for the comparison between the two groups. For these calculations you can assume that the denominator in the test statistic is 0.08, so Z is simply the difference in the means divided 0.08. Note that you are performing 13 significance tests in this exercise. Keep this in mind when you interpret your results. Write a report summarizing your work.
The stated instructions are very clear, and here is what you need to do. You are going to compare the mean responses between the two age groups for each of the 13 questions. Your Null Hypothesis is this: the two means are equal. Your Alternative Hypothesis is this: the two means are not equal (two sided test).
HINT: For each question, calculate this z-statistic for each question: (mean of the younger group – mean of older group) divided by 0.08. The 0.08 is the standard deviation of the sampling distribution of the sample mean. For each of the 13 z-statistics, determine the P-value and say whether or not the difference is statistically significant at the 5 percent level (alpha = .05).
You can organize your results neatly in the following table with these columns:
Question Mean of Mean of z-value P-value Significance
Younger Grp Older Grp at 5% (Y/N)
----------- -------------- ------------ -------- -------- ------------
Item
50-64
65-79
Ambience:
Most restaurants to dark
2.75
2.93
Most restaurants to noisy
3.33
3.43
Background music often to loud
3.27
3.55
Restaurants are to smoky
3.17
3.12
Tables are too small
3.00
3.19
Tables are too close together
3.79
3.81
Menu design:
Print size not large enough
3.68
3.77
Glare makes menu hard to read
2.81
3.01
Color of menu make hard to read
2.53
2.72
Service:
It is hard to hear the service staff
2.65
3.00
I would rather be served
4.23
4.14
I would rather pay server
3.88
3.48
Service is too slow
3.13
3.10
Explanation / Answer
question mean of younger gp mean of older gp z p significance most restuarats to dark 2.75 2.93 -2.25 0.024448945 yes most restuarants tp noisy 3.33 3.43 -1.25 0.211299547 no background music often to loud 3.27 3.55 -3.5 0.000465258 yes restaurants to smoky 3.17 3.12 0.625 0.531971058 no rtables are too small 3 3.19 -2.375 0.01754895 yes tables are too close 3.79 3.81 -0.25 0.410068149 no menu design 0 1 no print size not large enough 3.68 3.77 -1.125 0.260589034 no glare makes menu hard to read 2.81 3.01 -2.5 0.012419331 yes color of menu make hard to read 2.53 2.72 -2.375 0.01754895 yes service 0 1 no it is hard to hear the service staff 2.65 3 -4.375 1.21432E-05 yes I would rather be served 4.23 4.14 1.125 0.260589034 no I would rather pay server 3.88 3.48 5 5.73303E-07 yes service too slow 3.13 3.1 0.375 0.707660467 no
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