It is known from past information that the average number of concussions per tea

Question

It is known from past information that the average number of concussions per team in the NFL is 9.5, with a population standard deviation of 3.04. Suppose we take a sample of 10 teams this year and find that the average number of concussions in the sample is 10.57. Is there evidence that there has been a significant increase in the number of concussions? Assume the distribution of the population of concussions is normal and use =.05

a. What are the null and alternative hypotheses?

b. What is the critical value

c. Calculate the test statistic.

d. Find the p-value

e. What conclusion is made here?

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   9.5  
Ha:    u   >   9.5   [ANSWER]

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b)
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha =    0.05          
zcrit =    +   1.644853627   [ANSWER]

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c)
Getting the test statistic, as              
              
X = sample mean =    10.57          
uo = hypothesized mean =    9.5          
n = sample size =    10          
s = standard deviation =    3.04          
              
Thus, z = (X - uo) * sqrt(n) / s =    1.113038519 [ANSWER]

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d)

Also, the p value is, as this is right tailed,              
              
p =    0.132845943   [ANSWER]      

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e)
              
As P > 0.05, we   FAIL TO REJECT THE NULL HYPOTHESIS.  

There is no significant increase in the number of concussions at 0.05 level. [CONCLUSION]

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