1. A study is being conducted at a large university to find out if there is any relationship between how a person travels to the university each day and what their position at university is. A random sample of 351 students, 50 lecturers, and 99 general staff is collected. These people are asked what their most common mode of transport is when traveling to university. The options are car, bike/walk, public transport, or 'other'. The results of this survey are presented below:
|
46
|
30
|
29
|
105
|
|
99
|
5
|
30
|
134
|
|
176
|
9
|
29
|
214
|
|
30
|
6
|
11
|
47
|
|
351
|
50
|
99
|
500
|
A χ2 test was conducted to test the hypotheses:
H0: There is no relationship between mode of transport and place at university.
H1: There is a relationship between mode of transport and place at university.
Assuming the null hypothesis is true, the following table of expected frequencies was created:
|
73.710
|
10.500
|
20.790
|
|
94.068
|
13.400
|
26.532
|
|
150.228
|
21.400
|
42.372
|
|
32.994
|
4.700
|
9.306
|
Calculate the test statistic (χ2) for this test. Give your answer to 3 decimal places.
χ2 =