Currently patrons at the library speak at an average of 64 decibels. Will this average decline after the installation of a new computer plug in station? After the plug in station was built, the librarian randomly recorded 47 people speaking at the library. Their average decibel level was 63.2 and their standard deviation was 5. What can be concluded at the the α α = 0.05 level of significance?

The conclusion is that the average level of decibel at the library has changed since the installation of a new computer plug

Step-by-step explanation:

From the question we are told that

     The  population mean is  

     The sample size is

      The sample mean is  

      The sample  standard deviation is  

       The level of significance is

The Null Hypothesis is  

The Alternative Hypothesis is  

The  test statistics is mathematically evaluated as

substituting values

The  negative sign show that this is a left-tail test

Now the critical value of the level of significance obtained from the critical values table is  

Now  comparing the critical value of the and the test statistics we see that  critical value is greater than the test statistic which implies that the null hypothesis is rejected.

The conclusion is that the average level of decibel at the library has changed since the installation of a new computer plug