I am curious whether people get a better workout in the morning or at night. To find out, I got volunteers from my boxing gym. 10 of us wore heartrate monitors during our workouts and each of us worked out once in the morning and once in the evening and recorded the number of calories we burned during each workout. At a significance level of 0.01, I want to prove that less calories are burned during morning workouts than during evening workouts. The morning workout sample is and the evening workout sample is. Below is a table displaying the data: Morning Workout 1,449 calories Member (Subject) Evening Workout 1 887 çalories 1,005 calories 912 calories 1,153 calories 1,168 calories 797 calories 4 458 calories 5 1,326 calories 1,160 calories 838 calories 929 calories 1,129 calories 1,347 calories 1,007 calories 808 calories 8 949 calories 9. 735 calories 10 853 calories 1.007 calories The R Output for the hypothesis test is below: One Sample t-test data: workoutdiff t= 0.17213, df= 9, p-value = 0.5664 alternative hypothesis: true mean less than 0 99 percent confidence interval: -Inf 157.2675 sample estimates: mean of x 13.5
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.
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