horrupavinvo

2022-03-01

A flight attendant selects a random sample of 201 travelers. For each, he records the class in which the person travels and whether they have carry-on luggage. He would like to know if there is convincing evidence that the class in which a person travels is associated with having carry-on luggage. Let $\alpha =0.05$.
What are the hypotheses for this test?
a.${H}_{0}$: Class is not independent of carry-on luggage. ${H}_{\alpha }$: Class is independent of carry-on luggage.
b. ${H}_{0}$: Class is independent of carry-on luggage. ${H}_{\alpha }$: Class is not independent of carry-on luggage.
c. ${H}_{0}$: There is an association between class and carry-on luggage. ${H}_{\alpha }$: There is no association between class and carry-on luggage.
d. ${H}_{0}$: The proportion of travelers who have carry-on luggage is not the same in the types of class. ${H}_{\alpha }$: The proportion of travelers who have carry-on luggage is the same in the types of class.

Zernerqcw

In order to determine whether the class in which person travels is independent of whether they have carry-on luggage or not, a chi-square test of independence needs to be conducted.
In this test, there will be two types of counts, one is expected counts (denoted by E) and other is observed or actual counts (denoted by O).
The test will determine whether the actual counts are significantly different from the expected count or not. If the test shows that there is evidence of significant difference in between them, then it can be concluded that the test is significant.
The null hypothesis for the chi-square test of independence claims that there is no association between the variables or the two variables are independent of each other.
The alternate hypothesis for the chi-square test of independence claims that there is association between the variables or the two variables are not independent of each other.
This suggests that first option, third option and fourth option are incorrect.
In this case the two variables are: Class and Carry-on luggage.
The null hypothesis for the chi-square test of independence claims that the class is independent of carry-on luggage.
The alternate hypothesis for the chi-square test of independence claims that the class is not independent of carry-on luggage.
The null hypothesis and the alternate hypothesis are mentioned below.
${H}_{0}$: Class is independent of carry-on luggage.
${H}_{\alpha }$: Class is not independent of carry-on luggage.
Hence, second option is correct option.

Do you have a similar question?