An American medical team wishes to test whether passive smoking affects the chance of children contracting bronchitis. Historically, the disease has been known to occur at least once in 20% of children aged 12. The team analysed the results of a random sample of 250 12-year-old children who were passive smokers, and found that 30 of these had contracted bronchitis at least once in their lives. Use a 5% level of significance to test the claim that the proportion of children who are passive smokers is 20%. What is the null and alternate hypotheses What is the value of the test statistic from below z = 3.16 z = -3.16 z =3.89 z = -3.89 What is the p-value from below 0.0016 0.0008 0.0000 0.0001 Based on this evidence, what is the conclusion
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.
An American medical team wishes to test whether passive smoking affects the chance of children contracting bronchitis. Historically, the disease has been known to occur at least once in 20% of children aged 12.
The team analysed the results of a random sample of 250 12-year-old children who were passive smokers, and found that 30 of these had contracted bronchitis at least once in their lives.
Use a 5% level of significance to test the claim that the proportion of children who are passive smokers is 20%.
- What is the null and alternate hypotheses
-
What is the value of the test statistic from below
z = 3.16 z = -3.16 z =3.89 z = -3.89 -
What is the p-value from below
0.0016 0.0008 0.0000 0.0001 Based on this evidence, what is the conclusion
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