Many students at Matt's school claim they can think more clearly while listening to their favorite kind of music. Matt thinks music interferes with thinking clearly. To test this, he recruits 84 volunteers and randomly assigns them to two groups: The "Music" group listens to their favorite music while playing a "matching" memory game. The "No Music" group plays the same game in silence. Below are summary statistics for the number of turns each subject took to complete the game (fewer turns indicate better performance): Music: 15.833 No music: 13.714 (a) Is there convincing evidence that listening to music increases the number of turns required to finish the memory game? (b) Suppose Matt allowed people to choose whether or not they were in the group that listened to music while playing the game? Give an example of a problem that might arise if the subjects were allowed to do this.
Added by Nicole P.
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Null hypothesis (H0): There is no difference in the number of turns required to finish the game between the Music and No Music groups (μ1 - μ2 = 0). Alternative hypothesis (H1): Listening to music increases the number of turns required to finish the game (μ1 - Show more…
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Does listening to music while studying hinder students' learning? Two AP Statistics students designed an experiment to find out. They selected a random sample of 30 students from their medium-sized high school to participate. Each subject was given 10 minutes to memorize two different lists of 20 words, once while listening to music and once in silence. The order of the two word lists was determined at random; so was the order of the treatments. The difference in the number of words recalled (music- silence) was recorded for each subject. A paired $t$ test on the differences yielded $t=-3.01$ and $P$ -value $=0.0027$ (a) State appropriate hypotheses for the paired $t$ test. Be sure to define your parameter. (b) What are the degrees of freedom for the paired $t$ test? (c) Interpret the $P$ -value in context. What conclusion should the students draw? (d) Describe a Type I error and a Type II error in this setting. Which mistake could students have made based on your answer to part (c)?
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Tests about a Population Mean
Music and memory Does listening to music while studying help or hinder students’ learning? Two AP Statistics students designed an experiment to find out. They selected a random sample of 30 students from their medium-sized high school to participate. Each subject was given 10 minutes to memorize two different lists of 20 words, once while listening to music and once in silence. The order of the two word lists was determined at random; so was the order of the treatments. A boxplot of the differences in the number of words recalled (music silent) is shown below, along with some Minitab output from a one-sample t test. Perform a complete analysis of the students’ data. Include a confidence interval.
Sri K.
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