Questions: Fake Twitter followers: Many celebrities and public figures have Twitter accounts with large numbers of followers. However, some of these followers are fake, resulting from accounts generated by spamming computers. In a sample of 44 twitter audits, the mean percentage of fake followers was 13.8 with a standard deviation of 9.4. Part: 0 / 2 Part 1 of 2 Construct a 90% interval for the mean percentage of fake Twitter followers. Round the answers to one decimal place. A 90% confidence interval for the mean percentage of fake Twitter followers is <μ< .

Fake Twitter followers: Many celebrities and public figures have Twitter accounts with large numbers of followers. However, some of these followers are fake, resulting from accounts generated by spamming computers. In a sample of 44 twitter audits, the mean percentage of fake followers was 13.8 with a standard deviation of 9.4.

Part: 0 / 2

Part 1 of 2

Construct a 90% interval for the mean percentage of fake Twitter followers. Round the answers to one decimal place. A 90% confidence interval for the mean percentage of fake Twitter followers is <μ< .

Transcript text: Fake Twitter followers: Many celebrities and public figures have Twitter accounts with large numbers of followers. However, some of these followers are fake, resulting from accounts generated by spamming computers. In a sample of 44 twitter audits, the mean percentage of fake followers was 13.8 with a standard deviation of 9.4 . Part: $0 / 2$ Part 1 of 2 Construct a $90 \%$ interval for the mean percentage of fake Twitter followers. Round the answers to one decimal place. A $90 \%$ confidence interval for the mean percentage of fake Twitter followers is $\square$ $<\mu<$ $\square$ .

Solution

Solution Steps

Step 1: Given Data

We are provided with the following data:

Sample size ($n$) = 44
Sample mean ($\bar{x}$) = 13.8
Sample standard deviation ($s$) = 9.4
Confidence level = 90%

Step 2: Calculate the Significance Level

The significance level ($\alpha$) is calculated as: \[ \alpha = 1 - \text{confidence level} = 1 - 0.90 = 0.10 \]

Step 3: Determine the Z-Score

For a 90% confidence level, the Z-score corresponding to $\alpha/2 = 0.05$ can be found in Z-tables or using statistical software. The Z-score is approximately: \[ z \approx 1.645 \]

Step 4: Calculate the Margin of Error

The margin of error (ME) is calculated using the formula: \[ \text{ME} = z \cdot \frac{s}{\sqrt{n}} = 1.645 \cdot \frac{9.4}{\sqrt{44}} \approx 1.6 \]

Step 5: Construct the Confidence Interval

The confidence interval is constructed using the sample mean and the margin of error: \[ \text{Confidence Interval} = \left( \bar{x} - \text{ME}, \bar{x} + \text{ME} \right) = \left( 13.8 - 1.6, 13.8 + 1.6 \right) = (12.2, 15.4) \]