Number of Words in a Novel The National Novel Writing Association states that the average novel is at least 50,000 words. A particularly ambitious writing club at a college-preparatory high school had randomly selected members with works of the following lengths, At $\alpha=0.05$, is there sufficient evidence to conclude that the mean length is greater than 50,000 words? Assume that the population is approximately normally distributed.
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Part 1 of 5
(a) State the hypotheses and identify the claim.
\[
\begin{array}{l}
H_{0}: \square \text { (Choose one) } \mathbf{\nabla} \\
H_{1}: \square \text { (Choose one) } \mathbf{\nabla}
\end{array}
\]
This hypothesis test is a (Choose one) $\mathbf{V}$ test.
Answer
\(\boxed{H_{0}: \mu = 50000, H_{1}: \mu > 50000}\)
Step 1 ：State the hypotheses and identify the claim.
Step 2 ：The null hypothesis (H0) is that the mean length of the novels is equal to 50,000 words: \(H_{0}: \mu = 50000\).
Step 3 ：The alternative hypothesis (H1) is that the mean length of the novels is greater than 50,000 words: \(H_{1}: \mu > 50000\).
Step 4 ：This hypothesis test is a one-tailed test because we are only interested in whether the mean is greater than 50,000, not if it is less than or equal to.
Step 5 ：\(\boxed{H_{0}: \mu = 50000, H_{1}: \mu > 50000}\)
