Question

QUESTION: I believe that most (more than half) of all Reynolds students are from this area, and have been so since birth. From a numerical point of view, I think that more than half of all Reynolds students have lived in at most 2 cities in their lifetime. Use our class data as a sample to perform a test to determine if I am correct. Test at a .20 level of significance.

CLASS DATA:

Number of cities lived in:

22 cities- 1 person

17 cities- 1 person

12 cities - 1 person

11 cities - 1 person

25 cities - 1 person

28 cities - 1 person

16 cities - 1 person

14 cities - 1 person

20 cities- 1 person

9 cities- 2 people

8 cities- 5 people

7 cities - 7 people

6 cities - 9 people

5 cities - 19 people

4 cities - 27 people

3 cities - 42 people

2 cities - 61 people

1 city - 78 people

Reynolds Student:

Yes- 60

No- 201

Total Number of Occupants - 261

Answer 1

The hypothesis being tested is:

H₀: p = 0.5

H_a: p > 0.5

p̂ = (61 + 78)/261 = 0.5326

The test statistic, z = (p̂ - p)/√p(1-p)/n

z = (0.5326 - 0.5)/√0.5(1-0.5)/261

z = 1.05

The p-value is 0.1463.

Since the p-value (0.1463) is less than the significance level (0.20), we can reject the null hypothesis.

Therefore, we can conclude that more than half of all Reynolds students have lived in at most 2 cities in their lifetime.

Please give me a thumbs-up if this helps you out. Thank you!