21 In many ways I find myself happy that I dont have to ride

21. In many ways I find myself happy that I don\'t have to ride a subway on a regular basis. On a 96-degree day in New York City, the hottest subway platform was 106.6 degrees. So WNYC decided to get some information. They sampled 97 platforms during the evening rush this summer to measure the temperature. All were south of Central Park and most in Manhattan. From their data the found an average of 81.31 degrees with a standard deviation of 7.05 degrees. (Source: http://www.wnyc.org/story/hottest-subway-stations-map-nyc/ (Links to an external site.))

21a. There had been a number of complaints on social media that subway platforms in NYC were easily over 100 degrees on a regular basis in the summer. Given the data collected above, at the 0.01 level, can you say that the average temperature on a NYC subway platform in summer is greater than 100 degrees? Show work as stated in the quiz directions.

Solution

Formulating the null and alternative hypotheses,          
          
Ho:   u   =   100
Ha:    u   <   100
          
As we can see, this is a    1   tailed test.  
          
Thus, getting the critical z, as alpha =    0.01   ,  
          
zcrit =    2.326347874      

Thus, rejection region is when z > 2.326.
          
Getting the test statistic, as          
          
X = sample mean =    81.31      
uo = hypothesized mean =    100      
n = sample size =    97      
s = standard deviation =    81.31      
          
Thus, z = (X - uo) * sqrt(n) / s =    -2.263868556              
          
Comparing z and zcrit, we   FAIL TO REJECT THE NULL HYPOTHESIS.  

We have no sufficient evidence that the average temperature on a NYC subway platform in summer is greater than 100 degrees. [CONCLUSION]