Questions: Are costumed internet theater troupes or personal storytellers more expressive?

Are costumed internet theater troupes or personal storytellers more expressive?
Transcript text: Are costumed internet theater troupes or personal storytellers more expressive?
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Solution

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Solution Steps

Step 1: Identify the given information
  • Sample size (\(n\)) = 135
  • Sample mean (\(\bar{x}\)) = 1.98
  • Population standard deviation (\(\sigma\)) = 0.9
  • Confidence level = 99.98%
Step 2: Determine the z-score for the given confidence level

For a 99.98% confidence level, the z-score is approximately 3.90 (this can be found using a z-table or standard normal distribution table).

Step 3: Calculate the margin of error (E)

The margin of error (E) is calculated using the formula: \[ E = z \times \frac{\sigma}{\sqrt{n}} \] \[ E = 3.90 \times \frac{0.9}{\sqrt{135}} \] \[ E = 3.90 \times \frac{0.9}{11.62} \] \[ E = 3.90 \times 0.0774 \] \[ E \approx 0.30 \]

Step 4: Construct the confidence interval

The confidence interval is calculated using the formula: \[ \text{Confidence Interval} = \bar{x} \pm E \] \[ \text{Confidence Interval} = 1.98 \pm 0.30 \] \[ \text{Confidence Interval} = (1.68, 2.28) \]

Final Answer

The 99.98% confidence interval for the mean number of personal computers is (1.68, 2.28).

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