2. Tip-Of-The-Toungue Phenomenon A journal published a study of the “tip-of-the-tognue" phe- nomenon, trying to think of a word that you know, but can't instantly retrieve, in senior citizens. The researchers compared 100 people between 60 and 72 years of age with 100 between 73 and 83 years of age. When primed with the initial syllable of a missing word, the younger seniors had a higher recall rate. Suppose 66 of the 100 seniors in the younger group could recall the word when primed with the initial syllable, while only 44 of the 100 seniors in the older group could recall the word. At a = 0.05, test the claim that younger seniors (age 60-72) have a HIGHER recall rate THAN older seniors (age 73-83). (Complete Parts (a), (b), and (c).) (a) The value of the test statistic z (rounded to four decimal places) is (i) -0.8136 (ii) 3.1269 (iii) -1.1119 (iv) 1.2623 (b) The p-value (rounded to four decimal places) is (i) 0.7921 (ii) 0.0018 (iii) 0.0009 (iv) 0.1034 You should find one of the following useful for Part (b): P(2 > -0.8136) = 0.7921 P(2 > 3.1269) = 0.0009 P(z > -1.1119) z 0.8669 P(z > 1.2623) = 0.1034 (c) State your conclusion. (i) Fail to reject the null hypothesis. There is insufficient evidence to conclude that the recall rate of younger seniors is higher than the recall rate of the older seniors. (ii) Fail to reject the null hypothesis. There is sufficient evidence to conclude that the recall rate of younger seniors is higher than the recall rate of the older seniors. (iii) Reject the null hypothesis. There is insufficient evidence to conclude that the recall rate of younger seniors is higher than the recall rate of the older seniors. (iv) Reject the null hypothesis. There is sufficient evidence to conclude that the recall rate of younger seniors is higher than the recall rate of the older seniors.
2. Tip-Of-The-Toungue Phenomenon A journal published a study of the “tip-of-the-tognue" phe- nomenon, trying to think of a word that you know, but can't instantly retrieve, in senior citizens. The researchers compared 100 people between 60 and 72 years of age with 100 between 73 and 83 years of age. When primed with the initial syllable of a missing word, the younger seniors had a higher recall rate. Suppose 66 of the 100 seniors in the younger group could recall the word when primed with the initial syllable, while only 44 of the 100 seniors in the older group could recall the word. At a = 0.05, test the claim that younger seniors (age 60-72) have a HIGHER recall rate THAN older seniors (age 73-83). (Complete Parts (a), (b), and (c).) (a) The value of the test statistic z (rounded to four decimal places) is (i) -0.8136 (ii) 3.1269 (iii) -1.1119 (iv) 1.2623 (b) The p-value (rounded to four decimal places) is (i) 0.7921 (ii) 0.0018 (iii) 0.0009 (iv) 0.1034 You should find one of the following useful for Part (b): P(2 > -0.8136) = 0.7921 P(2 > 3.1269) = 0.0009 P(z > -1.1119) z 0.8669 P(z > 1.2623) = 0.1034 (c) State your conclusion. (i) Fail to reject the null hypothesis. There is insufficient evidence to conclude that the recall rate of younger seniors is higher than the recall rate of the older seniors. (ii) Fail to reject the null hypothesis. There is sufficient evidence to conclude that the recall rate of younger seniors is higher than the recall rate of the older seniors. (iii) Reject the null hypothesis. There is insufficient evidence to conclude that the recall rate of younger seniors is higher than the recall rate of the older seniors. (iv) Reject the null hypothesis. There is sufficient evidence to conclude that the recall rate of younger seniors is higher than the recall rate of the older seniors.
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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:2. Tip-Of-The-Toungue Phenomenon A journal published a study of the "tip-of-the-tognue" phe-
nomenon, trying to think of a word that you know, but can't instantly retrieve, in senior citizens. The
researchers compared 100 people between 60 and 72 years of age with 100 between 73 and 83 years of
age. When primed with the initial syllable of a missing word, the younger seniors had a higher recall rate.
Suppose 66 of the 100 seniors in the younger group could recall the word when primed with the initial
syllable, while only 44 of the 100 seniors in the older group could recall the word. At a = 0.05, test the
claim that younger seniors (age 60-72) have a HIGHER recall rate THAN older seniors (age 73-83).
(Complete Parts (a), (b), and (c).)
(a) The value of the test statistic z4 (rounded to four decimal places) is
(i) -0.8136
(ii) 3.1269
(iii) -1.1119
(iv) 1.2623
(b) The p-value (rounded to four decimal places) is
(i) 0.7921
(ii) 0.0018
(iii) 0.0009
(iv) 0.1034
You should find one of the following useful for Part (b):
P(2 > -0.8136) 0.7921 P(2 > 3.1269) = 0.0009 P(2 > -1.1119) z 0.8669 P(z > 1.2623) = 0.1034
(c) State your conclusion.
(i) Fail to reject the null hypothesis. There is insufficient evidence to conclude that the recall rate of
younger seniors is higher than the recall rate of the older seniors.
(ii) Fail to reject the null hypothesis. There is sufficient evidence to conclude that the recall rate of
younger seniors is higher than the recall rate of the older seniors.
(iii) Reject the null hypothesis. There is insufficient evidence to conclude that the recall rate of younger
seniors is higher than the recall rate of the older seniors.
(iv) Reject the null hypothesis. There is sufficient evidence to conclude that the recall rate of younger
seniors is higher than the recall rate of the older seniors.
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