Math

StatisticsQ&A LibraryA 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.Question

Asked Mar 21, 2019

736 views

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.

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* H _{0}*. 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* H _{a}*.

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 ...

Tagged in

Find answers to questions asked by student like you

Show more Q&A

Q: A normal distribution has a mean of 10 and a standard deviation of 10. What is the number such that ...

A: The given information is that the scores distributed normally with mean 10 and variance is 49. The s...

Q: Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advan...

A: The provided information are:

Q: Test the hypotheses of Ho: sigma is equal to 0.56 versus Ha: sigma not equal to 0.56 using a 5% sign...

A: According to the given question, to test the hypothesis of H0: sigma is equal to 0.56 versus Ha: sig...

Q: Using the table below, determine the critical value or values for a hypothesis test for a proportion...

A: It is provided that the test is right tailed and the significance level is 1%.So, the critical value...

Q: Find the critical value and rejection region for the type of t-test with level of significance α an...

A: Note:Hey! Thank you for posting the question. Since you have not mentioned the purpose for which the...

Q: A statistical program is recommended. Electromagnetic technologies offer effective nondestructive se...

A: Hey, since there are multiple subparts posted, we will answer first three subparts. If you want any ...

Q: 4 (continued). Currently, Melvin has equipped the Club of Ad Hominem. 20% of the time he swings the ...

A: The given information is not sufficient to solve all the subparts. More information is required to s...

Q: Why should researchers be very cautious about comparison or correlatios that involve different vaiab...

A: In general correlation does not imply causation. If there is strong correlation between two variable...

Q: Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of ...

A: Hello. Since your question has multiple sub-parts, we will solve the first three sub-parts for you. ...