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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
134
176
9
214
6
11
47
351
50
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 =
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