Math  /  Data & Statistics

Question```latex \text{Homework } \mathbf{f} \, 5: 9(1,3,4,5) \, 14(1,2) \\ \text{Question 10 of 30 (1 point) I Question Attempt: 1 of 3} \\ \text{Jonathan} \\ 6 \\ 7 \\ 8 \\ \checkmark 9 \\ 10 \\ 11 \\ 12 \\ 13 \\ 14 \\ 15 \\ 16 \\ \text{Españ} \\ 17 \\
\text{Spam: A researcher reported that } 71.8\% \text{ of all email sent in a recent month was spam. A system manager at a large corporation believes that the percentage at his company may be } 77\%. \text{ He examines a random sample of 500 emails received at an email server, and finds that 364 of the messages are spam. Can you conclude that the percentage of emails that are spam differs from } 77\% \text{? Use both } \alpha=0.01 \text{ and } \alpha=0.05 \text{ levels of significance and the } P\text{-value method with the TI-84 Plus calculator.}
\text{Part 1 of 5} \\ \text{(a) State the appropriate null and alternate hypotheses.} \\ H_{0}: \square^{\infty} \\
\text{Part 3 of 5} \\ \text{(c) Compute the } P\text{-value. Round the answer to at least four decimal places.} \\ P\text{-value }=0.05^{\otimes} \\
\text{Correct Answer:} \\ P\text{-value }=0.0256 \\
\text{Part 4 of 5} \\ \text{(d) Determine whether to reject } H_{0}. \\
\text{At the } \alpha=0.01 \text{ level, do not reject } \nabla \text{ the null hypothesis } H_{0}. \\ \text{At the } \alpha=0.05 \text{ level, reject } \quad \boldsymbol{r} \text{ the null hypothesis } H_{0}. \\
\text{Part: } 4 / 5 \\
\text{Part 5 of 5} \\ \text{(e) State a conclusion.} \\
\text{At the } \alpha=0.01 \text{ level of significance, there } \square \text{ enough evidence to conclude that the percentage of emails that are spam differs from } 77\%. \\ \text{At the } \alpha=0.05 \text{ level of significance, there } \square \text{ (Choose one) enough evidence to conclude that the percentage of emails that are spam differs from } 77\%. \\ \text{Skip Part} \\ \text{Check} \\ \text{Save For Later} \\ \text{Submit Assignment}

Studdy Solution
State the conclusion:
- At the α=0.01\alpha = 0.01 level of significance, there is not enough evidence to conclude that the percentage of emails that are spam differs from 77%. - At the α=0.05\alpha = 0.05 level of significance, there is enough evidence to conclude that the percentage of emails that are spam differs from 77%.

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