We are learning about z tests, t tests, and chi squared tests. I am a bit confus
ID: 3219853 • Letter: W
Question
We are learning about z tests, t tests, and chi squared tests. I am a bit confused about how to tell which test to conduct depending on the wording of a problem and how these tests are different and what they test for. Here is an example question:
A local zoo is interested in knowing if age is a factor when choosing to enter the aquarium. As patrons enter the zoo, a random sample are asked their age and whether or not they intend to visit the aquarium. Data is shown in the table below; please perform a test to determine if age makes a difference in their choice to enter the aquarium. Be sure to give an interpretation with your answer.
Ages
Enter Aquarium
Not Enter
Total
18>
53
27
80
18-40
72
58
130
40+
61
29
90
Total
186
114
300
Ages
Enter Aquarium
Not Enter
Total
18>
53
27
80
18-40
72
58
130
40+
61
29
90
Total
186
114
300
Explanation / Answer
H0: 1 = 2
H1: 1 2
People who enter the aquarium is 0.62. Therefore, we would expect the number of 18+ to enter the aquarium to be 80*0.62=49.6=50. We would calculate each of the values in the same fashion and put it in table as mentioned below:-
Ages
Enter Aquarium
Not Enter
Total
18>
53 (49.6)
27 (30.4)
80
18-40
72 (80.6)
58 (49.4)
130
40+
61 (55.8)
29 (34.2)
90
Total
186
114
300
2=(53-49.6)^2/49.6…………..(29-34.2)^2/34.2=4.30
DF would (r-1)(c-1)=2*1=2
critical value for 2 DF is 5.991 and our value is 4.30. Hence, we cannot reject the null hypothesis i.e age does not matter to enter the aquarium.
Ages
Enter Aquarium
Not Enter
Total
18>
53 (49.6)
27 (30.4)
80
18-40
72 (80.6)
58 (49.4)
130
40+
61 (55.8)
29 (34.2)
90
Total
186
114
300
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