Statistics can help decide the authorship of literary works. Sonnets by a certain Elizabethan poet are known to contain an average of 8.9 new words.

Statistics can help decide the authorship of literary works. Sonnets by a certain Elizabethan poet are known to contain an average of 8.9 new words. The standard deviation of the number of new words is 2.5. Now a manuscript with six new sonnets has come to light, and scholars are debating whether it is the poet's work. The sonnets contain an average of 10.2 words not used in the poet's known works. Assume the number of new words used by this poet in each poem is normally distributed. What can you say about the authorship?

Expert Solution

population mean(u)=8.9
standard deviation, sigma =2.5
sample mean, x =10.2
number (n)=6
null, Ho: μ=8.9
alternate, H1: μ!=8.9
level of significance, alpha = 0.05
from standard normal table, two tailed z alpha/2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 10.2-8.9/(2.5/sqrt(6)
zo = 1.2737
| zo | = 1.2737
critical value
the value of |z alpha| at los 5% is 1.96
we got |zo| =1.2737 & | z alpha | = 1.96
make decision
hence value of |zo | < | z alpha | and here we do not reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != 1.2737 ) = 0.2028
hence value of p0.05 < 0.2028, here we do not reject Ho
ANSWERS
---------------
null, Ho: μ=8.9
alternate, H1: μ!=8.9
test statistic: 1.2737
critical value: -1.96 , 1.96
decision: do not reject Ho
p-value: 0.2028
we do not have enough evidence to support the claim that the authorship of literary works.

orchestra answered 2 years ago

For each statement, decide whether descriptive or inferential statistics is used. a. The average life expectancy in New Zealand is 78.49 years (Source: World Factbook).

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Statistics can help decide the authorship of literary works. Sonnets by a certain Elizabethan poet are known to contain an average of 8.9 new words.

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For each statement, decide whether descriptive or inferential statistics is used. a. The average life expectancy in New Zealand is 78.49 years (Source: World Factbook).