1 Sugyswe sonnets by Shakespeare are known to contain an ave

1. Sugyswe sonnets by Shakespeare are known to contain an average of-65 new words (words not previously used in his sonnets). The standard deviation of the new words is a- 2.7. A new manuscript with 5 new sonnets is found and scholars are debating whether or not it belongs to Shakespeare. The new sonnets contain an averageo S S new words not used previously by Shakespeare. The scholars argue that the new manuscript is written by an unknown author. Is there enough evidence to say that new sonnets were not written by Shakespeare? [hint: Is the sepulation mean different) a. What assumptions) distribution you will need to find this evidence? 12 pts) b Perform an appropriate test of significance and make sure you include the hypotheses, test statistic, P-value, and conclusions when -0.1 and = 0.01. [8 pts] e. What is the role of a? [Upts)

Solution

1.

a)

We need to assume that the new sonnets ahve a normally distributed number of new words.

b)

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   6.5  
Ha:    u   =/   6.5  
              
As we can see, this is a    two   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    8.8          
uo = hypothesized mean =    6.5          
n = sample size =    5          
s = standard deviation =    2.7          
              
Thus, t = (X - uo) * sqrt(n) / s =    1.904798647          

Here,

df = n - 1 =    4          

              
Thus, the p value is              
              
p =    0.129520119          
              
As P > 0.01 and P > 0.10, we   FAIL TO REJECT THE NULL HYPOTHESIS at both 0.10 and 0.01 levels.

Thus, there is no significant evidence that the new sonnets were not written by Shakespeare at both 0.10 and 0.01 levels. [CONCLUSION]

c)

alpha states how \"strict\" we are in rejecting the null hypothesis. It determine what probability is \"rare enough\" so that we wouldn\'t consider it as just happening by chance.

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