Number of Words in a Novel The National Novel Writing Associ

Number of Words in a Novel: The National Novel Writing Association states that the average novel is at least 50,000 words. A particularly ambitious writing club at college-preparatory high school had randomly selected members with works of the following lengths. At x=0.10, is greater than 50,000 words?

48,972, 49,800, 50,100, 50,020, 51,560, 49,900, and 52,193

Solution

Getting the mean and standard deviations of these data,

X (mean) = 50363.57143
s (standard deviation) = 1113.159446

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   50000  
Ha:    u   >   50000  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    6          
tcrit =    +   1.439755747      
              
Getting the test statistic, as              
              
X = sample mean =    50363.57143          
uo = hypothesized mean =    50000          
n = sample size =    7          
s = standard deviation =    1113.159446          
              
Thus, t = (X - uo) * sqrt(n) / s =    0.864134595          
              
Also, the p value is              
              
p =    0.210356142          
              
Comparing t and tcrit (or, p >0.10), we   FAIL TO REJECT THE NULL HYPOTHESIS.          
Thus, there is no significant evidence at 0.10 level that the mean of this data set is greater than 50000 words. [CONCLUSION]