Question

The following data give noise levels measured at 25 different times directly outside of Grand Central Station in Manhattan.

82, 89, 94, 110, 74, 122, 112, 95, 100, 78, 65, 60, 90, 83, 87, 75, 114, 85, 69, 94, 124, 115, 107, 88, 97

Use this data to test the null hypothesis that the average noise level directly outside of Grand Central Station is less than or equal to 80 decibels. Hint: compute the p-value and make a reasonable decision based on that

Answer 1

Null hypothesis

$H_{0}:\mu \leq 80$

vs

Alternative hypothesis

$H_{1}:\mu > 80$

We have given,

Population mean =80

Sample mean =92.36

Sample standard deviation=17.5164

Sample size =25

t test statistic formula is

$t=\frac{\bar{x}-\mu }{\frac{s}{\sqrt{n}}}$

   $=\frac{92.36-80}{\frac{17.5164}{\sqrt{25}}}$

=3.528

Degree of freedom =n-1= 24

P value=0.00086.....................by using =TDIST(3.528,24,1)

P value 0.00086 < 0.05

Therefore, we reject H0.

We have sufficient evidence to say that,the average noise level directly outside of Grand Central Station is greater than 80 decibels