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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 8.88 new words (words not used in the poet's other works). The standard deviation of the number of new words is 3. Now a manuscript with 6 new sonnets has come to light, and scholars are debating whether it is the poet's work. The new sonnets contain an average of 12.4 words not used in the poet's known works. We expect poems by another author to contain more new words, so to see if we have evidence that the new sonnets are not by our poet we test the following hypotheses.
H0 : µ = 8.88 vs Ha : µ > 8.88
Give the z test statistic and its P-value. What do you conclude about the authorship of the new poems? (Let a = .05.)
Use 2 decimal places for the z-score and 4 for the p-value.
a.What is z ?
b.The p-value is greater than ?
c. What is the conclusion? A)The sonnets were written by another poet or b) There is not enough evidence to reject the null.
Answer:
a) z = 2.87
b) P-value ≈ 0.0021
c) The sonnets were written by another poet
Step-by-step explanation:
We are given the hypothesis as;
Null hypothesis; H0 : µ = 8.88
Alternative hypothesis; Ha : µ > 8.88
We are also given;
Sample size; n = 6
Population Standard deviation; σ = 3
Sample mean; x¯ = 12.4
a) formula for z - value is;
z = (x¯ - µ)/(σ/√n)
z = (12.4 - 8.88)/(3/√6)
z = 2.87
b) we are given the significance value as α = 0.05.
From online p-value from z-score calculator attached and using z = 2.87; one tail distribution; α = 0.05, we have;
P-value = 0.002052
Approximating to 4 decimal places;
P-value ≈ 0.0021
c) The p-value is less than the significance level, thus we react the null hypothesis and conclude that the sonnets were written by another poet
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