A former residential complex was found to be a Superfund site polluted with several hazardous materials. Tamela is an investigative journalist who would like to show whether the proportion of the residents of the complex who eventually died from cancer is greater than the regional average of 14%. She randomly selects 54 residents who lived in the complex and finds that 12 of those residents eventually died from cancer. Are all of the conditions for this hypothesis test met, and if so, what are the null and alternative hypotheses for this hypothesis test?Select the correct answer below: Although the proportion follows a binomial model with two independent outcomes and the data are selected at random, the number of successes and the number of failures are not both greater than or equal to 5. Although the proportion follows a binomial model with two independent outcomes and the number of successes and the number of failures are both greater than or equal to 5, the data are not selected at random. Although the data are selected at random and the number of successes and the number of failures are both greater than or equal to 5, the proportion does not follow a binomial model. All of the conditions to conduct the hypothesis test have been met. The null and alternative hypotheses are {H0:p=0.14Ha:p<0.14. All of the conditions to conduct the hypothesis test have been met. The null and alternative hypotheses are {H0:p=0.14Ha:p>0.14. All of the conditions to conduct the hypothesis test have been met. The null and alternative hypotheses are {H0:p=0.14Ha:p≠0.14.

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Asked Mar 21, 2019
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A former residential complex was found to be a Superfund site polluted with several hazardous materials. Tamela is an investigative journalist who would like to show whether the proportion of the residents of the complex who eventually died from cancer is greater than the regional average of 14%. She randomly selects 54 residents who lived in the complex and finds that 12 of those residents eventually died from cancer. Are all of the conditions for this hypothesis test met, and if so, what are the null and alternative hypotheses for this hypothesis test?

Select the correct answer below:

 

Although the proportion follows a binomial model with two independent outcomes and the data are selected at random, the number of successes and the number of failures are not both greater than or equal to 5.

 

Although the proportion follows a binomial model with two independent outcomes and the number of successes and the number of failures are both greater than or equal to 5, the data are not selected at random.

 

Although the data are selected at random and the number of successes and the number of failures are both greater than or equal to 5, the proportion does not follow a binomial model.

 

All of the conditions to conduct the hypothesis test have been met. The null and alternative hypotheses are {H0:p=0.14Ha:p<0.14.

 

All of the conditions to conduct the hypothesis test have been met. The null and alternative hypotheses are {H0:p=0.14Ha:p>0.14.

 

All of the conditions to conduct the hypothesis test have been met. The null and alternative hypotheses are {H0:p=0.14Ha:p≠0.14.

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Expert Answer

Step 1

Null Hypothesis:

A null hypothesis is a statement regarding the population value which one has to prove or disprove based on facts. It can be denoted as H0. Most often null hypothesis states that there is no significant relation between population values.

Alternative Hypothesis:

An alternative hypothesis is a contradictory statement of null hypothesis. It can be denoted as Ha.

Step 2

Identifying the null and alternative hypotheses:

Define the random variable X as the proportion of the residents of the complex who eventually died from cancer. Here, a random sample (n) of 54 residents who lived in the complex. Since the selection is random, each resident is independent of the other. Also, there are two possible outcomes, the residents of the complex who eventually died from cancer or not (success or failure). It was found that out of the 54 residents 12 of the residents were eventually died from cancer. Thus, the probability of success (p) is 0.22. The probability of success remains same for all the trials. All the conditions for a binomial distribution are satisfied and hence, X follows binomial distribution.

That is, the proportion follows binomial model and the number of successes and the number of failures is greater than or equal to 5.

From the above findings, it can be observed that first three options are incorrect.

Step 3

The claim is that the proportion of the residents of the complex who eventually died from cancer is greater than the regional average of 14%. Thus, the null and alternative ...

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