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).

Question

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).

Accepted Answer

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