Sonnets by a certain poet are known to contain an average of 8.9 (words not used
ID: 3149984 • Letter: S
Question
Sonnets by a certain poet are known to contain an average of 8.9 (words not used in the poet's other works) 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 to the poet's work. The new sonnets contain an average of 10.2 words not used In the poet's known works. We expect the poems by another author to contain more new words. Use a level of significance of 4%. What is the alternative hypothesis? What is the test statistic value? What is the minimal sample mean to reject Ho? What is the P-value? What do you conclude about the authorship of the new poems? This answer has not boon grsuiod yot.Explanation / Answer
a)
Ha: u > 8.9 [ANSWER]
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b)
Formulating the null and alternative hypotheses,
Ho: u <= 8.9
Ha: u > 8.9
As we can see, this is a right tailed test.
Getting the test statistic, as
X = sample mean = 10.2
uo = hypothesized mean = 8.9
n = sample size = 6
s = standard deviation = 2.5
Thus, t = (X - uo) * sqrt(n) / s = 1.273734666 [ANSWER]
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c)
As
df = n - 1 = 5
Also, the p value is, as this is right tailed,
p = 0.129376931 [ANSWER]
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d)
As P > 0.04, we fail to reject Ho.
There is no significant evidence that these new sonnets have a mean number of new words greater than 8.9, hence, no significant evidence that these are from another author. [CONCLUSION]
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