A poll surveyed people in six countries to assess attitudes toward a variety of alternate forms of energy. Suppose the data in the following table are a portion of the poll's findings concerning whether people favor or oppose the building of new nuclear power plants. Response Country Great Britain France Italy Spain Germany United States Strongly favor 133 161 128 141 298 204 Favor more than oppose 222 367 272 348 309 326 Oppose more than favor 311 334 322 381 219 316 Strongly oppose 443 215 389 217 221 174 (a) How large was the sample in this poll? =____ (b) Conduct a hypothesis test to determine whether people's attitude toward building new nuclear power plants is independent of country. State the null and alternative hypotheses. H0: The attitude toward building new nuclear power plants is not mutually exclusive of the country. Ha: The attitude toward building new nuclear power plants is mutually exclusive of the country. H0: The attitude toward building new nuclear power plants is mutually exclusive of the country. Ha: The attitude toward building new nuclear power plants is not mutually exclusive of the country. H0: The attitude toward building new nuclear power plants is independent of the country. Ha: The attitude toward building new nuclear power plants is not independent of the country. H0: The attitude toward building new nuclear power plants is not independent of the country. Ha: The attitude toward building new nuclear power plants is independent of the country. Find the value of the test statistic. (Round your answer to two decimal places.) =____ Find the p-value. (Round your answer to four decimal places.) p-value = ____ State your conclusion. (A) Do not reject H0. We cannot conclude that the attitude toward building new nuclear power plants is independent of the country. (B) Do not reject H0. We conclude that the attitude toward building new nuclear power plants is not independent of the country. (C) Reject H0. We cannot conclude that the attitude toward building new nuclear power plants is independent of the country. (D) Reject H0. We conclude that the attitude toward building new nuclear power plants is not independent of the country. (c) Using the percentage of respondents who "strongly favor" and "favor more than oppose," which country has the most favorable attitude toward building new nuclear power plants? (A) Great Britain (B) France (C) Italy (D) Spain (E) Germany (F) United States Which country has the least favorable attitude? (A) Great Britain (B) France (C) Italy (D) Spain (E) Germany (F) United States
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
A poll surveyed people in six countries to assess attitudes toward a variety of alternate forms of energy. Suppose the data in the following table are a portion of the poll's findings concerning whether people favor or oppose the building of new nuclear power plants.
| Response | Country | |||||
|---|---|---|---|---|---|---|
| Great Britain |
France | Italy | Spain | Germany | United States |
|
| Strongly favor | 133 | 161 | 128 | 141 | 298 | 204 |
| Favor more than oppose | 222 | 367 | 272 | 348 | 309 | 326 |
| Oppose more than favor | 311 | 334 | 322 | 381 | 219 | 316 |
| Strongly oppose | 443 | 215 | 389 | 217 | 221 | 174 |
(a) How large was the sample in this poll? =____
(b) Conduct a hypothesis test to determine whether people's attitude toward building new nuclear power plants is independent of country.
State the null and alternative hypotheses.
H0: The attitude toward building new nuclear power plants is not mutually exclusive of the country.
Ha: The attitude toward building new nuclear power plants is mutually exclusive of the country.
H0: The attitude toward building new nuclear power plants is mutually exclusive of the country.
Ha: The attitude toward building new nuclear power plants is not mutually exclusive of the country.
H0: The attitude toward building new nuclear power plants is independent of the country.
Ha: The attitude toward building new nuclear power plants is not independent of the country.
H0: The attitude toward building new nuclear power plants is not independent of the country.
Ha: The attitude toward building new nuclear power plants is independent of the country.
Find the value of the test statistic. (Round your answer to two decimal places.) =____
Find the p-value. (Round your answer to four decimal places.)
p-value = ____
State your conclusion.
(A) Do not reject H0. We cannot conclude that the attitude toward building new nuclear power plants is independent of the country.
(B) Do not reject H0. We conclude that the attitude toward building new nuclear power plants is not independent of the country.
(C) Reject H0. We cannot conclude that the attitude toward building new nuclear power plants is independent of the country.
(D) Reject H0. We conclude that the attitude toward building new nuclear power plants is not independent of the country.
(c) Using the percentage of respondents who "strongly favor" and "favor more than oppose," which country has the most favorable attitude toward building new nuclear power plants?
(A) Great Britain
(B) France
(C) Italy
(D) Spain
(E) Germany
(F) United States
Which country has the least favorable attitude?
(A) Great Britain
(B) France
(C) Italy
(D) Spain
(E) Germany
(F) United States
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