(1) There is an equal number of red and blue marbles (H0), or (2) 60% of the marbles are blue (HA) Your task is to guess which of the two conditions is in fact true. As an aid, you are allowed to randomly select 10 marbles (one at a time, with replacement) and to record the colour of each marble as you take it out. You decide that if 7 or more of the 10 marbles you select are blue, you will conclude that condition 2 is true. a) If, in fact, condition 1 is true, what is the probability that you will erroneously conclude that condition 2 is true? b) If, in fact, condition 2 is true, what is the probability that you will erroneously conclude that condition 1 is true?
(1) There is an equal number of red and blue marbles (H0), or (2) 60% of the marbles are blue (HA) Your task is to guess which of the two conditions is in fact true. As an aid, you are allowed to randomly select 10 marbles (one at a time, with replacement) and to record the colour of each marble as you take it out. You decide that if 7 or more of the 10 marbles you select are blue, you will conclude that condition 2 is true. a) If, in fact, condition 1 is true, what is the probability that you will erroneously conclude that condition 2 is true? b) If, in fact, condition 2 is true, what is the probability that you will erroneously conclude that condition 1 is true?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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Question
A bag contains 100 marbles. Each marble is either red or blue. One of two conditions exists with respect to the number of red and blue marbles:
(1) There is an equal number of red and blue marbles (H0), or (2) 60% of the marbles are blue (HA)
Your task is to guess which of the two conditions is in fact true. As an aid, you are allowed to randomly select 10 marbles (one at a time, with replacement) and to record the colour of each marble as you take it out. You decide that if 7 or more of the 10 marbles you select are blue, you will conclude that condition 2 is true.
a) If, in fact, condition 1 is true, what is the probability that you will erroneously conclude that condition 2 is true?
b) If, in fact, condition 2 is true, what is the probability that you will erroneously conclude that condition 1 is true?
Answer:
1a) 0.172
b) 0.618
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