Questions: A researcher wishes to estimate the amount of time spent on social media per day. He will need to compute the minimum sample to accurately estimate this value. The population standard deviation is 0.82 hours per day, and he wishes the estimated mean to be within 0.10 hours per day. Using a confidence level of 95%, compute the minimum sample size.

Solution Steps

To find the Z-score corresponding to a \(95\%\) confidence level, we use the formula:

\[ Z = \text{PPF}\left(1 - \frac{1 - 0.95}{2}\right) = \text{PPF}(0.975) = 1.96 \]

The formula for calculating the sample size \(n\) is given by:

\[ n = \left(\frac{Z \cdot \sigma}{\text{Margin of Error}}\right)^2 \]

Substituting the values:

• \(Z = 1.96\)
• \(\sigma = 0.82\) (population standard deviation)
• \(\text{Margin of Error} = 0.10\)

We have:

\[ n = \left(\frac{1.96 \cdot 0.82}{0.1}\right)^2 = (1.96 \cdot 8.2)^2 = (16.112)^2 \approx 259.0 \]

Final Answer