MATLAB: An Introduction with Applications
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Determine test statistic and determine p value
Transcribed Image Text:### Hypothesis Testing in Dictionaries
A simple random sample of 10 pages from a dictionary is obtained. The numbers of words defined on those pages are found, with the results \( n = 10 \), \( \bar{x} = 55.3 \) words, \( s = 16.1 \) words. Given that this dictionary has 1459 pages with defined words, the claim that there are more than 70,000 defined words is equivalent to the claim that the mean number of words per page is greater than 48.0 words. Use a 0.01 significance level to test the claim that the mean number of words per page is greater than 48.0 words. What does the result suggest about the claim that there are more than 70,000 defined words? Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. Assume that the population is normally distributed.
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#### What are the null and alternative hypotheses?
**A.**
- \( H_0 \): \(\mu = 48.0\) words
- \( H_1 \): \(\mu > 48.0\) words
**B.**
- \( H_0 \): \(\mu = 48.0\) words
- \( H_1 \): \(\mu \neq 48.0\) words
**C.**
- \( H_0 \): \(\mu \ge 48.0\) words
- \( H_1 \): \(\mu < 48.0\) words
**D.**
- \( H_0 \): \(\mu = 48.0\) words
- \( H_1 \): \(\mu < 48.0\) words
The correct selection is option **A**:
- \( H_0 \): \(\mu = 48.0\) words
- \( H_1 \): \(\mu > 48.0\) words
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#### Determine the test statistic.
- (Round to two decimal places as needed.)
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