fake followers: many celebrities and public figures have social media accounts with large numbers of followers. however, some of these followers are fake, resulting from accounts generated by spamming computers. in a sample of 53 audits, the mean percentage of fake followers was 13.3 with a standard deviation of 9.8. use the ti-84 plus calculator as needed.

part: 0 / 2

part 1 of 2

(a) construct a 99.8% confidence interval for the mean percentage of fake followers. round the answers to at least one decimal place.

a 99.8% confidence interval for the mean percentage of fake followers is $\square

Question

fake followers: many celebrities and public figures have social media accounts with large numbers of followers. however, some of these followers are fake, resulting from accounts generated by spamming computers. in a sample of 53 audits, the mean percentage of fake followers was 13.3 with a standard deviation of 9.8. use the ti-84 plus calculator as needed.

part: 0 / 2

part 1 of 2

(a) construct a 99.8% confidence interval for the mean percentage of fake followers. round the answers to at least one decimal place.

a 99.8% confidence interval for the mean percentage of fake followers is $\square < \mu < \square$.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Confidence Interval for Mean", "t-Distribution Critical Value" ], "current_concepts": [ "Confidence Interval", "t-Distribution", "Margin of Error" ] } ## Identify the given sample statistics $$ \begin{aligned} n &= 53 \ \bar{x} &= 13.3 \ s &= 9.8 \ \text{Confidence Level} &= 99.8\% \implies \alpha = 0.002 \end{aligned} $$ ## Find the critical value $t_{\alpha/2}$ $$ \begin{aligned} df &= n - 1 = 52 \ t_{0.001, 52} &\approx 3.2464 \end{aligned} $$ ## Calculate the margin of error and confidence interval $$ \begin{aligned} E &= t_{\alpha/2} \cdot \frac{s}{\sqrt{n}} = 3.2464 \cdot \frac{9.8}{\sqrt{53}} \approx 4.370 \ \text{Lower limit} &= \bar{x} - E = 13.3 - 4.370 \approx 8.9 \ \text{Upper limit} &= \bar{x} + E = 13.3 + 4.370 \approx 17.7 \end{aligned} $$ A $99.8\%$ confidence interval for the mean percentage of fake followers is $8.9$ $< \mu <$ $17.7$. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Confidence Interval for Mean" ] }

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Question

Explanation:

Identify the given sample statistics

Find the critical value \(t_{\alpha/2}\)

Calculate the margin of error and confidence interval

Answer: