1. A study was conducted to investigate the effectiveness of hypnotism in reducing pain. Results for randomly selected subjects are shown in the table below. A lower score indicates less pain. The "before" value is matched to an "after" value and differences are calculated (after minus before; I ask you to com- plete the table by computing these differences). Assume the population of differences is approximately normal. Are the sensory measurements, on average, lower after hypnotism? Test at a 2.5% significance level. Subject: After Before Difference B| C|D|E | F | G | H_ 6.9 1.9 7.7 8.7 8.7 5.6 3.0 2.1 6.7 6.0 9.3 10.5 11.9 7.6 5.9 11.7 (a) Complete the table above, by computing the differences. (b) Provide the null and alternative hypotheses for this hypothesis test. Ho: Ha: (c) The test statistic t= (round to two decimal places as needed) (d) The p-value p= (round to four decimal places as needed) (e) State your conclusion: REJECT or FAIL TO REJECT Ho. At a 2.5% level of significance, there is SUFFICIENT or INSUFFICIENT evidence to conclude that the sensory measurements, on average, are lower after hypnotism. (Circle the correct capitalized word or phrase in each of the two places a choice is given.)
1. A study was conducted to investigate the effectiveness of hypnotism in reducing pain. Results for randomly selected subjects are shown in the table below. A lower score indicates less pain. The "before" value is matched to an "after" value and differences are calculated (after minus before; I ask you to com- plete the table by computing these differences). Assume the population of differences is approximately normal. Are the sensory measurements, on average, lower after hypnotism? Test at a 2.5% significance level. Subject: After Before Difference B| C|D|E | F | G | H_ 6.9 1.9 7.7 8.7 8.7 5.6 3.0 2.1 6.7 6.0 9.3 10.5 11.9 7.6 5.9 11.7 (a) Complete the table above, by computing the differences. (b) Provide the null and alternative hypotheses for this hypothesis test. Ho: Ha: (c) The test statistic t= (round to two decimal places as needed) (d) The p-value p= (round to four decimal places as needed) (e) State your conclusion: REJECT or FAIL TO REJECT Ho. At a 2.5% level of significance, there is SUFFICIENT or INSUFFICIENT evidence to conclude that the sensory measurements, on average, are lower after hypnotism. (Circle the correct capitalized word or phrase in each of the two places a choice is given.)
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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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Transcribed Image Text:1. A study was conducted to investigate the effectiveness of hypnotism in reducing pain. Results for
randomly selected subjects are shown in the table below. A lower score indicates less pain. The "before"
value is matched to an "after" value and differences are calculated (after minus before; I ask you to com-
plete the table by computing these differences). Assume the population of differences is approximately
normal. Are the sensory measurements, on average, lower after hypnotism? Test at a 2.5% significance
level.
A | B | C | D
6.9 1.9 7.7 8.7
6.7 6.0
FGH
Subject:
After
Before
Difference
E
8.7 5.6 3.0 2.1
10.5 11.9 7.6 5.9 11.7
9.3
(a) Complete the table above, by computing the differences.
(b) Provide the null and alternative hypotheses for this hypothesis test.
Ho:
Ha:
(c) The test statistic t =
(round to two decimal places as needed)
(а) The p-value p -
(round to four decimal places as needed)
(e) State your conclusion: REJECT or FAIL TO REJECT H9. At a 2.5% level of significance, there is
SUFFICIENT or INSUFFICIENT evidence to conclude that the sensory measurements, on average, are
lower after hypnotism. (Circle the correct capitalized word or phrase in each of the two places a choice is
given.)
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