Question

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?

Answer 1

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

Explanation:

From the question we are told that

The population mean is
`\mu = 64`

The sample size is
`n = 47`

The sample mean is
`\= x = 63.2`

The sample standard deviation is
`\sigma = 5`

The level of significance is
`\alpha = 0.05`

The Null Hypothesis is

`H_o : \mu = 64`

The Alternative Hypothesis is

`H_a : \mu \\e 64`

The test statistics is mathematically evaluated as

`t = (\= x - \mu )/((\sigma )/(√(n) ) )`

substituting values

`t = (63.1 - 64 )/((5 )/(√(47) ) )`

`t = -1.234`

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

`z_(0.05) = 1.645`

Now comparing the critical value of the
`\alpha` 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