Homework SourseA study was conducted to determine whether bigcity and small
A study was conducted to determine whether big-city and small-town dwellers differed in their helpfulness to strangers. In this study, the investigators rang the doorbells of strangers living in New York City or small towns in the vicinity. They explained they had misplaced the address of a friend living in the neighborhood and asked to use the phone. The following data show the number of individuals who admitted or did not admit the strangers (the investigators) into their homes:
Do Big city dwellers differ in their helpfulness to strangers? Use a=0.05 in making your decision
Helpfulness to Strangers
Admitted Strangers into their homes
Did not Admit Strangers into their home
Totals
Big City Dwellers
60
90
150
Small Town Dwellers
70
30
100
Total
130
120
250
| Helpfulness to Strangers | Admitted Strangers into their homes | Did not Admit Strangers into their home | Totals |
| Big City Dwellers | 60 | 90 | 150 |
| Small Town Dwellers | 70 | 30 | 100 |
| Total | 130 | 120 | 250 |
Solution
A study was conducted to determine whether big-city and small-town dwellers differed in their helpfulness to strangers. In this study, the investigators rang the doorbells of strangers living in New York City or small towns in the vicinity. They explained they had misplaced the address of a friend living in the neighborhood and asked to use the phone. The following data show the number of individuals who admitted or did not admit the strangers (the investigators) into their homes:
Do Big city dwellers differ in their helpfulness to strangers? Use a=0.05 in making your decision
For this problem we can use chi square test or two sample proportion test
Chi square test is used here.
Null hypothesis: Big city dwellers not differ in their helpfulness to strangers
Alternate hypothesis: Big city dwellers differ in their helpfulness to strangers
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
C1
C2
Total
fo-fe
R1
60
90
150
-18
18
R2
70
30
100
18
-18
Total
130
120
250
Expected Frequencies
Column variable
Row variable
C1
C2
Total
(fo-fe)^2/fe
R1
78
72
150
4.1538
4.5
R2
52
48
100
6.2308
6.75
Total
130
120
250
Calculated chi square =
21.635
Level of Significance
0.05
Number of Rows
2
Number of Columns
2
Degrees of Freedom
1
Critical Value
3.841
Calculated chi square =21.635 >3.841 the table value
The null hypothesis is rejected.
We conclude that Big city dwellers differ in their helpfulness to strangers.
| Chi-Square Test | ||||||
| Observed Frequencies | ||||||
| Column variable | Calculations | |||||
| Row variable | C1 | C2 | Total | fo-fe | ||
| R1 | 60 | 90 | 150 | -18 | 18 | |
| R2 | 70 | 30 | 100 | 18 | -18 | |
| Total | 130 | 120 | 250 | |||
| Expected Frequencies | ||||||
| Column variable | ||||||
| Row variable | C1 | C2 | Total | (fo-fe)^2/fe | ||
| R1 | 78 | 72 | 150 | 4.1538 | 4.5 | |
| R2 | 52 | 48 | 100 | 6.2308 | 6.75 | |
| Total | 130 | 120 | 250 | |||
| Calculated chi square = | 21.635 | |||||
| Level of Significance | 0.05 | |||||
| Number of Rows | 2 | |||||
| Number of Columns | 2 | |||||
| Degrees of Freedom | 1 | |||||
| Critical Value | 3.841 |
