Is it a good idea to listen to music when studying for a big...

Is it a good idea to listen to music when studying for a big test? In a study conducted by some Statistics students, 62 people were randomly assigned to listen to rap music, music by Mozart, or no music while attempting to memorize objects pictured on a page. They were then asked to list all the objects they could remember. Here are summary statistics: $$\begin{array}{llll}{} & {\text { Rap }} & {\text { Mozart }} & {\text { No Music }} \\ {\text { Count }} & {29} & {20} & {13} \\ {\text { Mean }} & {10.72} & {10.00} & {12.77} \\ {\text { SD }} & {3.99} & {3.19} & {4.73}\end{array}$$ a) Does it appear that it is better to study while listening to Mozart than to rap music? Test an appropriate hypothesis and state your conclusion. b) Create a 90$\%$ confidence interval for the mean difference in memory score between students who study to Mozart and those who listen to no music at all. Interpret your interval.

Is it a good idea to listen to music when studying for a big test? In a study conducted by some Statistics students, 62 people were randomly assigned to listen to rap music, music by Mozart, or no music while attempting to memorize objects pictured on a page. They were then asked to list all the objects they could remember. Here are summary statistics:
$$\begin{array}{llll}{} & {\text { Rap }} & {\text { Mozart }} & {\text { No Music }} \\ {\text { Count }} & {29} & {20} & {13} \\ {\text { Mean }} & {10.72} & {10.00} & {12.77} \\ {\text { SD }} & {3.99} & {3.19} & {4.73}\end{array}$$
a) Does it appear that it is better to study while listening to Mozart than to rap music? Test an appropriate hypothesis and state your conclusion.
b) Create a 90$\%$ confidence interval for the mean difference in memory score between students who study to Mozart and those who listen to no music at all. Interpret your interval.

Key Concepts

Statistical Significance

Statistical significance refers to the likelihood that a result or relationship is caused by something other than random chance. It is determined by performing a statistical test and comparing the p-value to a predetermined significance level, indicating whether the observed differences between groups are reliable and not just due to sampling variability.

Confidence Interval

A confidence interval is a range of values derived from sample statistics that is likely to contain the true population parameter with a certain degree of confidence. For example, a 90% confidence interval suggests that if the same sampling procedure were repeated numerous times, approximately 90% of the intervals would be expected to capture the true difference in means.

Hypothesis Testing

Hypothesis testing is the process of evaluating two mutually exclusive statements about a population to determine which statement is better supported by sample data. It involves formulating a null hypothesis (typically stating no difference or effect) and an alternative hypothesis (stating the presence of a difference or effect), then using a statistical test to decide whether to reject the null hypothesis.

T-Test

A t-test is a statistical method used to compare the means of two groups when the variances are unknown and the sample sizes are relatively small. It employs the t-distribution to account for the uncertainty in the estimate of the standard error, making it suitable for testing hypotheses about the difference between two means.

Transcript

00:01 What's up, stat katz? so this is problem 46.

00:04 It says, is it a good idea to listen to music when studying for a big test? in a study conducted by some statistics students, 62 people were randomly assigned to listen to rap music, mozart, or no music while attempting to memorize objects pictured on a page.

00:19 They were then asked to list the objects they could remember.

00:23 We were given the summary statistics for that.

00:26 Part a says, does it appear that it is better to study while listening? to mozart than to rap music.

00:32 Test an appropriate hypothesis and state your conclusion.

00:36 Alright, so we want to know if it's better to listen to mozart than to wrap.

00:40 So our null hypothesis is always going to be that the mean differences are the same, so equal to zero.

00:49 But our alternative hypothesis is going to be that our mean differences are greater than zero because we're predicting that it's better to listen to mozart than to wrap.

00:59 So let's go ahead and pull out our calculator so we can crunch these numbers.

01:04 So we're going to go to tests.

01:06 We're going to go to two sample t test.

01:09 And we are going to enter mozart first and wrap second.

01:16 So wrap.

01:26 We want to have greater than, so that's good.

01:29 And we're going to hit calculate.

01:32 So our p value is equal to .76 if we round.

01:37 That is above 0 .05.

01:39 So we do not have a significant result.

01:48 So we fail to reject the null hypothesis because our p value is above our alpha level of 0 .05.

02:00 So we can't support our alternative because we fail to reject the null.