In a study conducted by some Statistics students, 63 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. The summary statistics for each group are shown in the table. Complete parts a and b. Rap Mozart No Music Count 31 19 13 Mean 10.68 9.83 13.56 SD 3.86 3.64 4.25 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. Let group M correspond to Mozart listeners and group R correspond to rap listeners. Write the null and alternative hypotheses. Choose the correct answer below. A. H0: μM−μR<0 HA: μM−μR=0 B. H0: μM−μR=0 HA: μM−μR≠0 C. H0: μM−μR=0 HA: μM−μR>0 D. H0: μM−μR=0 HA: μM−μR<0 Test the hypothesis. t=nothing (Round to two decimal places as needed.) P=nothing (Round to four decimal places as needed.) State your conclusion. Use α=0.05. ▼ Do not reject Reject H0. There ▼ is no is evidence that the mean number of objects remembered by those who listen to Mozart is higher than the mean number of objects remembered by those who listen to rap music. b) Now compare the group that listened to Mozart with the group that listened to no music. Create a 90% confidence interval for the mean difference in memory score between students who listen to Mozart and those who listen to no music at all. Interpret your interval. The 90% confidence interval for the negative difference in means is (nothing,nothing). (Round to three decimal places as needed.) Interpret the interval. Choose the correct answer below. A. With 90% confidence, the mean number of objects remembered by all subjects is in the interval. B. With 90% confidence, the mean number of objects remembered by those who listen to Mozart is lower than the mean number remembered by those who listen to no music by an amount in the interval. C. With 90% confidence, there is no difference between the mean number of objects remembered by those who listen to Mozart and the mean number of objects remembered by those who listen to no music.

In a study conducted by some Statistics students, 63 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. The summary statistics for each group are shown in the table. Complete parts a and b. Rap Mozart No Music Count 31 19 13 Mean 10.68 9.83 13.56 SD 3.86 3.64 4.25 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. Let group M correspond to Mozart listeners and group R correspond to rap listeners. Write the null and alternative hypotheses. Choose the correct answer below. A. H0: μM−μR<0 HA: μM−μR=0 B. H0: μM−μR=0 HA: μM−μR≠0 C. H0: μM−μR=0 HA: μM−μR>0 D. H0: μM−μR=0 HA: μM−μR<0 Test the hypothesis. t=nothing (Round to two decimal places as needed.) P=nothing (Round to four decimal places as needed.) State your conclusion. Use α=0.05. ▼ Do not reject Reject H0. There ▼ is no is evidence that the mean number of objects remembered by those who listen to Mozart is higher than the mean number of objects remembered by those who listen to rap music. b) Now compare the group that listened to Mozart with the group that listened to no music. Create a 90% confidence interval for the mean difference in memory score between students who listen to Mozart and those who listen to no music at all. Interpret your interval. The 90% confidence interval for the negative difference in means is (nothing,nothing). (Round to three decimal places as needed.) Interpret the interval. Choose the correct answer below. A. With 90% confidence, the mean number of objects remembered by all subjects is in the interval. B. With 90% confidence, the mean number of objects remembered by those who listen to Mozart is lower than the mean number remembered by those who listen to no music by an amount in the interval. C. With 90% confidence, there is no difference between the mean number of objects remembered by those who listen to Mozart and the mean number of objects remembered by those who listen to no music.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 7E: List the sample space of each experiment. Selecting a letter of the alphabet

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In a study conducted by some Statistics students,

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. The summary statistics for each group are shown in the table. Complete parts a and b.


	Rap	Mozart	No Music
Count	31		19	13
Mean	10.68		9.83	13.56
SD	3.86		3.64	4.25

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.

Let group M correspond to Mozart listeners and group R correspond to rap listeners. Write the null and alternative hypotheses. Choose the correct answer below.

H0:

μM−μR<0

HA:

μM−μR=0

H0:

μM−μR=0

HA:

μM−μR≠0

H0:

μM−μR=0

HA:

μM−μR>0

H0:

μM−μR=0

HA:

μM−μR<0

Test the hypothesis.

t=nothing

(Round to two decimal places as needed.)

P=nothing

(Round to four decimal places as needed.)

State your conclusion. Use

α=0.05.

▼

Do not reject

Reject

H0.

There

▼

is no

evidence that the mean number of objects remembered by those who listen to Mozart is higher than the mean number of objects remembered by those who listen to rap music.

b) Now compare the group that listened to Mozart with the group that listened to no music. Create a

90%

confidence interval for the mean difference in memory score between students who listen to Mozart and those who listen to no music at all. Interpret your interval.

The

90%

confidence interval for the negative difference in means is

(nothing,nothing).

(Round to three decimal places as needed.)

Interpret the interval. Choose the correct answer below.

With

90%

confidence, the mean number of objects remembered by all subjects is in the interval.

With

90%

confidence, the mean number of objects remembered by those who listen to Mozart is lower than the mean number remembered by those who listen to no music by an amount in the interval.

With

90%

confidence, there is no difference between the mean number of objects remembered by those who listen to Mozart and the mean number of objects remembered by those who listen to no music.

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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