Question

Disney wanted to know if the age distribution of visitors to Disney World was the same in 2019 as it has been historically. Historically, the age distribution of visitors to Disney World is: 60% children (under 18), 30% adults (18-64) and 10% elderly (65+). They randomly sampled 100 visitors and recorded their ages.

What are the appropriate null and alternative hypotheses for this scenario?

Group of answer choices

a. Ho: The expected distribution is not met.

Ha: phat_child=.6, phat_adult=.3, phat_elder=.1

b. Ho: The expected distribution is not met.

Ha: p_child=.6, p_adult=.3, p_elder=.1

c. Ho: p_child=.6, p_adult=.3, p_elder=.1

Ha: The expected distribution is not met.

d. Ho: phat_child=.6, phat_adult=.3, phat_elder=.1

Ha: The expected distribution is not met.

Answer 1

Null hypothesis:

Ho:The expected distribution is not met.

Alternative hypothesis:

H1: pchild=0.6,padult=0.3,pelder=0.1

i.e. P1=0.6,P2=0.3,P3=0.1

Answer 2

The appropriate null and alternative hypotheses for this scenario are:

b. Ho: The expected distribution is not met. Ha: pchild = 0.6, padult = 0.3, pelder = 0.1

Explanation:

• Ho (Null Hypothesis): The null hypothesis states that the age distribution of visitors to Disney World in 2019 is the same as it has been historically. In other words, the proportions of children, adults, and elderly visitors in 2019 are equal to the historical proportions of 60%, 30%, and 10%, respectively.

• Ha (Alternative Hypothesis): The alternative hypothesis states that the age distribution of visitors to Disney World in 2019 is not the same as it has been historically. It suggests that at least one of the proportions (pchild, padult, pelder) is different from its historical value.

Note: The null hypothesis typically assumes no change or no effect, while the alternative hypothesis suggests that there is a change or effect in the population being studied. In this case, the null hypothesis assumes the historical proportions are still valid, while the alternative hypothesis suggests that the proportions have changed in some way in 2019.

Answer 3

The appropriate null and alternative hypotheses for this scenario are:

a. Ho: The expected distribution is not met. Ha: phatchild = 0.6, phatadult = 0.3, phatelder = 0.1

In hypothesis testing, the null hypothesis (Ho) represents the assumption of no effect or no difference, while the alternative hypothesis (Ha) represents the claim we are trying to test, which contradicts the null hypothesis. In this case, the null hypothesis states that the age distribution of visitors to Disney World in 2019 is the same as historically (i.e., 60% children, 30% adults, and 10% elderly). The alternative hypothesis suggests that the age distribution is different from the historically expected values.

It is important to note that the alternative hypothesis is written in terms of sample proportions (phatchild, phatadult, phatelder) because the hypothesis test is based on sample data, and we are trying to determine if the observed proportions in the sample are significantly different from the historical proportions.