Question

Currently patrons at the library speak at an average of 65 decibels. Will this average change after the installation of a new computer plug in station? After the plug in station was built, the librarian randomly recorded 55 people speaking at the library. Their average decibel level was 66.9 and their standard deviation was 19. What can be concluded at the the αα = 0.01 level of significance?

1. For this study, we should use Select an answer t-test for a population mean z-test for a population proportion
2. The null and alternative hypotheses would be:

H0:H0:  ? μ p  ? ≠ > < =       

H1:H1:  ? μ p  ? < = ≠ >    

3. The test statistic ? z t  =  (please show your answer to 3 decimal places.)
4. The p-value =  (Please show your answer to 4 decimal places.)
5. The p-value is ? > ≤  αα
6. Based on this, we should Select an answer reject fail to reject accept  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest that the population mean decibal level has not significantly changed from 65 at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean decibel level at the library has changed since the plug in station was built.
   • The data suggest the populaton mean has significantly changed from 65 at αα = 0.01, so there is statistically significant evidence to conclude that the population mean decibel level at the library has changed since the plug in station was built.
   • The data suggest the population mean has not significantly changed from 65 at αα = 0.01, so there is statistically significant evidence to conclude that the population mean decibel level at the library has not changed since the plug in station was built.

Answer 1

a)

For this study, we should use Select an answer t-test for a population mean

b)

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 65
Alternative Hypothesis: μ ≠ 65

Rejection Region
This is two tailed test, for α = 0.01 and df = 54
Critical value of t are -2.67 and 2.67.
Hence reject H0 if t < -2.67 or t > 2.67

c)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (66.9 - 65)/(19/sqrt(55))
t = 0.742

d)

P-value Approach
P-value = 0.4613

e)
As P-value >= 0.01,

f)

fail to reject null hypothesis.

g)

The data suggest that the population mean decibal level has not significantly changed from 65 at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean decibel level at the library has changed since the plug in station was built.