Questions: Question 5 (1 point) The population standard deviation for the height of college basketball players is 3 inches. If we want to estimate 97% confidence interval for the population mean height of these players with a 0.6 margin of error, how many randomly selected players must be surveyed? (Round up your answer to nearest whole number)

Solution Steps

We are given the following parameters for estimating the population mean height of college basketball players:

• Population standard deviation ($\sigma$): $3$ inches
• Margin of error ($E$): $0.6$ inches
• Confidence level: $97\%$

For a $97\%$ confidence level, the Z-score ($Z$) corresponding to the critical value is approximately: $$Z \approx 2.17$$

Using the formula for the sample size ($n$): $$n = \left( \frac{Z \cdot \sigma}{E} \right)^2$$ Substituting the known values: $$n = \left( \frac{2.17 \cdot 3}{0.6} \right)^2$$

Calculating the numerator: $$Z \cdot \sigma = 2.17 \cdot 3 = 6.51$$ Now, substituting back into the formula: $$n = \left( \frac{6.51}{0.6} \right)^2 = \left( 10.85 \right)^2 \approx 117.6225$$

Since we need a whole number for the sample size, we round up: $$n \approx 118$$

Final Answer