Question

7.2.14 Does listening to music affect how many words you can memorize? Student researchers tried to answer this question by having 20 subjects listen to music while trying to memorize words and also had the same 20 subjects try to memorize words when not listening to music. They randomly determined which condition was done first for each of their subjects. Here are their hypotheses: Null: The average of the difference in number of words memorized (no music-with music) is 0 (ud-0). Alternative: The average of the difference in number of words memorized (no music - with music) is greater than 0 (ud> O) The students found the following results in terms of number of words memorized: No music With music Difference 12 9.6 2.84 2.4 3.62 Mean Standard deviation 3.46

A) What is the explanatory variable in this study? Is it categorical or quantitative? Number of words memorized, categorical/Listened to music or not, categorical/Number of words memorized, quantative/Listened to music or not

B) What is the response variable in this study? Is it categorical or quantitative? Number of words memorized, categorical/Listened to music or not, categorical/Number of words memorized, quantative/Listened to music or not

C) What is the observed statistic in this study? 2.4/12/2.84/3.62

D) Assuming a true null hypothesis, we simulated this study and found 1,500 mean differences that are shown in the null distribution below.

Based on where the observed statistic lies in this distribution, the p-value appears to be fairly small. True/False

E)  The standard deviation of the null distribution is 0.974. Use this to find the standardized statistic for this test. Round your answer to 3 decimal places, e.g. 5.836.

_________

F) Based on your standardized statistic from part (e), is there strong evidence that people can memorize words better when music is not playing compared to when it is? No, the standardized statistic is less than 1/Yes, standardized statistic is more than 1/ No, standardized statistic is less than 2/Yes, standardized statistic is more than 2

Answer 1

A) The explanatory variable here is - 'Listening to music or not' and it is categorical in nature.

B) The response variable here is - 'Number of words memorized' and the variable is quantitative in nature.

C) The observed statistic is 2.4 which is mean difference between number of words memorized by those who did not listen music and those who did.

D) True, the observed statistic is 2.4 which is more than 2 times standard deviation (0.974) away from mean (-0.0090)

E) given standard deviation of null distribution as 0.974,

The standardized statistic is,

F) Yes, there is strong evidence that people can memorize words better when there is no music playing. because standardized statistic is more than 2.