Management at a radio station wants to know the number of songs it plays per hou

Question

Management at a radio station wants to know the number of songs it plays per hour. A random sample over the past month yields the following counts for songs per hour: 9, 13, 12, 8, 7, 10, 11, 10, 8, 12, 13, 9, 10, 12 and 11

The station doesn't think they play 10 songs per hour, but the owner doesn't know whether the station plays more or less than 10 songs per hour

A. What are the null and alternative hypotheses for this test?

B. Calculate the test statistic and p-value. Show work

C. What is the critical t value and what is the conclusion at significance level=.05?

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   10  
Ha:    u   =/   10   [HYPOTHESES]

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b)
              
As we can see, this is a    two   tailed test.      
              
df = n - 1 =    14          
              
Getting the test statistic, as              
              
X = sample mean =    10.33333333          
uo = hypothesized mean =    10          
n = sample size =    15          
s = standard deviation =    1.877181271          
              
Thus, t = (X - uo) * sqrt(n) / s =    0.687730305 [TEST STATISTIC]          
              
Also, the p value is              
              
p =    0.502858346   [P VALUE]

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c)      

Thus, getting the critical t,      

df = n - 1 =    14  

tcrit =    +/-   2.144786688 [CRITICAL VALUES]
              
As |t| < 2.14479, we   FAIL TO REJECT THE NULL HYPOTHESIS.          

There is no significant evidence at 0.05 level that the true mean songs per hour is not 10.

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