A survey by the National Institutes of Health asked a random sample of young adults (aged 19 to 25 years), “Where do you live now? That is, where do you stay most often?” Here is the full two-way table (omitting a few who refused to answer and one who claimed to be homeless):

a) Should we use a chi-square test for homogeneity or a chi-square test of association/independence in this setting? Justify your answer.

(b) State appropriate hypotheses for performing the type of test you chose in part (a). Minitab output from a chi-square test is shown below

(c) Check that the conditions for carrying out the test are met.

(d) Interpret the P-value in context. What conclusion would you draw?

Given in the question that, A survey by the National Institutes of Health asked a random sample of young adults (aged 19 to 25 years), “Where do you live now? That is, where do you stay most often?” Here is the full two-way table (omitting a few who refused to answer and one who claimed to be homeless):

We need to verify that should we use a chi-square test for homogeneity or a chi-square test of association/independence in this setting

The result is:

For the two qualitative variables of one sample, a two-way table was calculated. As a result, the chi-square test of independence/association should be applied in this situation.

Given in the question that, A survey by the National Institutes of Health asked a random sample of young adults (aged 19 to 25 years), “Where do you live now? That is, where do you stay most often?” Here is the full two-way table (omitting a few who refused to answer and one who claimed to be homeless):

We need to state appropriate hypotheses for performing the type of test chose in part (a)

For the above test, the proper null and alternative hypotheses could be expressed as follows:

$H_0$: There is no connection between the two variables.

$H_a$: A connection exists between two variables.

Given in the question that, A survey by the National Institutes of Health asked a random sample of young adults (aged 19 to 25 years), “Where do you live now? That is, where do you stay most often?” Here is the full two-way table (omitting a few who refused to answer and one who claimed to be homeless):

We need to find that whether the conditions for carrying out the test are met.

The following are the circumstances in this case:

1. A random sample is picked.

2. All of the projected counts are more than five.

3. The sample size is $10\%$lower than the population.

As a result, the required conditions might be considered to be met.

Given in the question that, A survey by the National Institutes of Health asked a random sample of young adults (aged 19 to 25 years), “Where do you live now? That is, where do you stay most often?” Here is the full two-way table (omitting a few who refused to answer and one who claimed to be homeless):

We need to interpret the P-value.

If there is no correlation between the variables, the probability of obtaining the same or extreme sample is $1.2$percent, with a $p$-value of $0.05$. The null hypothesis is found to be false. Thus, there is adequate evidence to reject the assertion that the two variables are related at the$5$ percent significance level.