SEE PICTURES AS WELLA researcher predicts that listening to music while solving math problems will make a particular brain area more active. To test this, a research participant has her brain scanned while listening to music and solving math problems, and the brain area of interest has a percentage signal of 59 . From many previous studies with this same math problems procedure (but not listening to music), it is known that the signal change in this brain area is normally distributed with a mean of 33 and a standard deviation of 10 . Complete parts (a) and (b) below.(b) Explain your answer to someone who has never had a course in statistics (but who is familiar with mean, standard deviation, and Z scores). A.Since the sample's score wasmoreextreme than the cutoff sample score(s), that means the probability of that score occurring, given that the null hypothesis is true, islessthan 0.01. With this knowledge, one canfail to rejectthe null hypothesis. B.Since the sample's score waslessextreme than the cutoff sample score(s), that means the probability of that score occurring, given that the null hypothesis is true, isgreaterthan 0.01. With this knowledge, one canrejectthe null hypothesis. C.Since the sample's score wasmoreextreme than the cutoff sample score(s), that means the probability of that score occurring, given that the null hypothesis is true, islessthan 0.01. With this knowledge, one canrejectthe null hypothesis. (a) Using a 0.01 level, what should the researcher conclude? First determine the null hypothesis. Choose the correct answer below.O A. Listening to music while solving math problems will make a particular brain area less active than while not listening to music.B. Listening to music while solving math problems will make a particular brain area more active than while not listening to music.O C. Listening to music while solving math problems will result in a percentage signal of 59, while not listening to music will result in a percentage signal of 33.O D. Listening to music while solving math problems will make a particular brain area less active than, or have the same activity as, while not listening to music.Determine the research hypothesis. Choose the correct answer below.O A. Listening to music while solving math problems will make a particular brain area less active than, or have the same activity as, while not listening to music.O B. Listening to music while solving math problems will make a particular brain area more active than while not listening to music.OC. Listening to music while solving math problems will make a particular brain area less active than while not listening to music.O D. Listening to music while solving math problems will result in a percentage signal of 59, while not listening to music will result in a percentage signal of 33.Determine the comparison distribution. Choose the correct answer below.Rectangular distributionNormal distributionSkewed distribution Determine the cutoff sample score(s).The cutoff sample score(s) is/are(Use a comma to separate answers as needed. Round to two decimal places as needed.)Determine the sample's score on the comparison distribution.The sample's score on the comparison distribution is(Round to two decimal places as needed.)Decide whether to reject the null hypothesis. Choose the correct answer below.A. Fail to reject the null hypothesis because the sample's score is more extreme than the cutoff sample score(s).B. Reject the null hypothesis because the sample's score is less extreme than the cutoff sample score(s).O C. Fail to reject the null hypothesis because the sample's score is less extreme than the cutoff sample score(s).O D. Reject the null hypothesis because the sample's score is more extreme than the cutoff sample score(s).

a) Correct Null hypothesis is option D. Correct research hypothesis is option B. Comparison…

Answered: Determine the cutoff sample score(s).…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 4AGP

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SEE PICTURES AS WELL

A researcher predicts that listening to music while solving math problems will make a particular brain area more active. To test this, a research participant has her brain scanned while listening to music and solving math problems, and the brain area of interest has a percentage signal of 59 . From many previous studies with this same math problems procedure (but not listening to music), it is known that the signal change in this brain area is normally distributed with a mean of 33 and a standard deviation of 10 . Complete parts (a) and (b) below.

(b) Explain your answer to someone who has never had a course in statistics (but who is familiar with mean, standard deviation, and Z scores).

Since the sample's score was

extreme than the cutoff sample score(s), that means the probability of that score occurring, given that the null hypothesis is true, is

less

than 0.01. With this knowledge, one can

fail to reject

the null hypothesis.

Since the sample's score was

less

extreme than the cutoff sample score(s), that means the probability of that score occurring, given that the null hypothesis is true, is

greater

than 0.01. With this knowledge, one can

reject

the null hypothesis.

Since the sample's score was

extreme than the cutoff sample score(s), that means the probability of that score occurring, given that the null hypothesis is true, is

less

than 0.01. With this knowledge, one can

reject

the null hypothesis.

Determine the cutoff sample score(s).
The cutoff sample score(s) is/are
(Use a comma to separate answers as needed. Round to two decimal places as needed.)
Determine the sample's score on the comparison distribution.
The sample's score on the comparison distribution is
(Round to two decimal places as needed.)
Decide whether to reject the null hypothesis. Choose the correct answer below.
A. Fail to reject the null hypothesis because the sample's score is more extreme than the cutoff sample score(s).
B. Reject the null hypothesis because the sample's score is less extreme than the cutoff sample score(s).
O C. Fail to reject the null hypothesis because the sample's score is less extreme than the cutoff sample score(s).
O D. Reject the null hypothesis because the sample's score is more extreme than the cutoff sample score(s).

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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