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wrote...
Posts: 248
3 weeks ago
Textbook authors must be careful that the reading level of their book is appropriate for the target audience. Some methods of assessing reading level require estimating the average word length. We've randomly chosen 20 words from a randomly selected page in Stats: Modeling the World and counted the number of letters in each word:

5, 5, 2, 11, 1, 5, 3, 8, 5, 4, 7, 2, 9, 4, 8, 10, 4, 5, 6, 6



Suppose that our editor was hoping that the book would have a mean word length of 6.5 letters. Does this sample indicate that the authors failed to meet this goal? Test an appropriate hypothesis and state your conclusion.
Textbook 

Stats: Modeling the World


Edition: 4th
Authors:
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3 weeks ago
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H0: μ = 6.5. The mean word length in the book is 6.5 words.
Ha: μ ≠ 6.5. The mean word length in the book is not 6.5 words.
* Randomization Condition: We have a random sample of the words in the book.
* 10% Condition: The words are less than 10% of all words in the book.
* Nearly Normal Condition: A histogram of the observed word lengths looks roughly unimodal and symmetric, so the population of all word lengths may be approximately Normal.
Since the conditions are satisfied, we will use a two-tail, one-sample t-test.

n = 20 = 5.5
s = 2.685 df = 19
t = = -1.67
P = 2 ∙ P(t19 < -1.67) = 0.11

Because the P-value is so high we do not reject the null hypothesis. This sample does not provide evidence that the average word length differs from the goal of 6.5 letters.
This verified answer contains over 4140 words.
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3 weeks ago
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