Currently, patrons at the library speak at an average of 69 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 44 people speaking at the library. Their average decibel level was 67.7 and their standard deviation was 19. What can be concluded at the α = 0.05 level of significance?
For this study, we should use a t-test for a population mean.
The null and alternative hypotheses would be:
H0: μ = 69
H1: μ ≠ 69
The test statistic t = (please show your answer to 3 decimal places.)
The p-value = (Please show your answer to 4 decimal places.)
The p-value is ≤ α.
Based on this, we should fail to reject the null hypothesis.
Thus, the final conclusion is that the data suggest that the population mean decibel level has not significantly changed from 69 at α = 0.05, 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.