In a science fair project, Emily conducted an experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, and then she asked the therapists to identify the selected hand by placing their hand just under Emily's hand without seeing it and without touching it. Among 310 trials, the touch therapists were correct 149 times. Complete parts (a) through (d). a, Given that Emily used a coin toss to select either her right hand or her left hand, what proportion correct responses would be expected if the touch therapists made random guesses? |(Type an integer or a decimal. Do not round.) b. Using Emily's sample results, what is the best point estimate of the therapists' success rate? (Round to three decimal places as needed.) c. Using Emily's sample results, construct a 95% confidence interval estimate of the proportion of correct responses made by touch therapists |
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.
![In a science fair project, Emily conducted an experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand,
and then she asked the therapists to identify the selected hand by placing their hand just under Emily's hand without seeing it and without touching it. Among 310 trials, the touch therapists were correct 149 times.
Complete parts (a) through (d).
a. Given that Emily used a coin toss to select either her right hand or her left hand, what proportion of correct responses would be expected if the touch therapists made random guesses?
(Type an integer or a decimal. Do not round.)
b. Using Emily's sample results, what is the best point estimate of the therapists' success rate?
(Round to three decimal places as needed.)
c. Using Emily's sample results, construct a 95% confidence interval estimate of the proportion of correct responses made by touch therapists.
|<p< (Round to three decimal places as needed.)
d. What do the results suggest about the ability of touch therapists to select the correct hand by sensing energy fields?
A. Since the confidence interval is not entirely below 0.5, there appears to be evidence that touch therapists can select the correct hand by sensing energy fields.
B. Since the confidence interval is not entirely above 0.5, there does not appear to be sufficient evidence that touch therapists can select the correct hand by sensing energy fields.
O C. Since the upper confidence limit is above 0.5, there appears to be evidence that touch therapists can select the correct hand by sensing energy fields.
D. Since the lower confidence limit is below 0.5, there does not appear to be sufficient evidence that touch therapists can select the correct hand by sensing energy fields.
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