A group of 9 concertgoers was selected at random. Before the concert they were given a hearing test, and then given another one after the concert. (The volume varied during the test, and the subject also had to state which ear the sound was in.) Here are the number of correctly identified sounds out of 10, both before and after theconcert.At the 0.05 level of significance, test a person’s hearing is worse after being affected by the noise of a concert.PersonABCDEFGHIBefore9109889998After8896671085

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Asked Dec 9, 2019
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A group of 9 concertgoers was selected at random. Before the concert they were given a hearing test, and then given another one after the concert. (The volume varied during the test, and the subject also had to state which ear the sound was in.) Here are the number of correctly identified sounds out of 10, both before and after theconcert.

At the 0.05 level of significance, test a person’s hearing is worse after being affected by the noise of a concert.

Person

A

B

C

D

E

F

G

H

I

Before

9

10

9

8

8

9

9

9

8

After

8

8

9

6

6

7

10

8

5

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Expert Answer

Step 1

The appropriate Null and Alternative Hypotheses are given below:

 

From the given information, the claim of the problem is the person’s hearing is worse after being affected by the noise of a concert.

 

Null hypothesis:

 

H0: µbefore= µafter.

 

That is, the person’s hearing is same for before and after being affected by the noise of a concert.

 

Alternative hypothesis:

 

H1: µafter< µbefore.

 

That is, the person’s hearing is worse after being affected by the noise of a concert.

 

Here, the hearing test is given for same persons are compared. Hence, the appropriate test for given testing is paired t test.

 

The test statistic is -3.266 and it is obtained below:

 

Excel Procedure:

 

  1. Enter the data for before and after...
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Image Transcriptionclose

t-Test: Paired Two Sample for Means Variable 1 Variable 2 Mean 7.444444444 8.777777778 Variance 2.527777778 0.444444444 Observations Pearson Correlation 0.694488704 Hypothesized Mean Difference df t Stat P(T<=t) one-tail -3.265986324 0.005712277 t Critical one-tail 1.859548038 P(T<=t) two-tail t Critical two-tail 0.011424554 2.306004135

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