Final answer:
In this case, the chi-square test was not performed in the question. Therefore, we cannot determine whether the type of flight and whether someone brought carry-on luggage are independent or dependent.
The correct answer is: c) The relationship cannot be determined.
Step-by-step explanation:
To determine whether the type of flight and whether someone brought carry-on luggage are independent or dependent, we can perform a chi-square test of independence using the provided data.
First, let's calculate the expected frequencies for each category under the assumption of independence. We can do this by multiplying the row total and column total, and then dividing by the overall total:
Expected frequency = (row total * column total) / overall total
For example, the expected frequency for "Connecting flight" and "Carry-on luggage" is (100 * 120) / 210 = 57.14.
Next, we calculate the chi-square test statistic:
chi-square = Σ [(observed frequency - expected frequency)² / expected frequency]
Summing up all the terms, we get the chi-square value.
Finally, we compare the obtained chi-square value to the critical value from the chi-square distribution table with (r - 1) * (c - 1) degrees of freedom, where r is the number of rows and c is the number of columns.
If the obtained chi-square value is greater than the critical value, we reject the null hypothesis of independence. Otherwise, we fail to reject the null hypothesis and conclude that the type of flight and whether someone brought carry-on luggage are independent.
Given the provided data, the chi-square test was not performed in the question. Therefore, we cannot determine whether the type of flight and whether someone brought carry-on luggage are independent or dependent.
The correct answer is: c) The relationship cannot be determined.
Your question is incomplete, but most probably the full question was:
A researcher wants to know whether there is a relationship between type of flight (connecting or direct) and whether someone brought carry-on luggage (yes or no). Data on 210 passengers is shown below.
Connecting flight Direct flight Total
Carry-on luggage 80 40 120
No carry-on luggage 20 70 90
Total 100 110 210
Are type of flight and whether someone brought carry-on luggage independent? (See the methods to check for independence from your lecture notes.) If they are not independent, discuss the relationship.
a) Yes, they are independent.
b) No, they are dependent.
c) The relationship cannot be determined.
d) They are related in a nonlinear manner.