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)

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)
Transcript text: 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) Answer: $\square$ A)
failed

Solution

failed
failed

Solution Steps

Step 1: Given Information

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

  • Population standard deviation (σ \sigma ): 3 3 inches
  • Margin of error (E E ): 0.6 0.6 inches
  • Confidence level: 97% 97\%
Step 2: Determine the Z-score

For a 97% 97\% confidence level, the Z-score (Z Z ) corresponding to the critical value is approximately: Z2.17 Z \approx 2.17

Step 3: Calculate the Required Sample Size

Using the formula for the sample size (n n ): n=(ZσE)2 n = \left( \frac{Z \cdot \sigma}{E} \right)^2 Substituting the known values: n=(2.1730.6)2 n = \left( \frac{2.17 \cdot 3}{0.6} \right)^2

Calculating the numerator: Zσ=2.173=6.51 Z \cdot \sigma = 2.17 \cdot 3 = 6.51 Now, substituting back into the formula: n=(6.510.6)2=(10.85)2117.6225 n = \left( \frac{6.51}{0.6} \right)^2 = \left( 10.85 \right)^2 \approx 117.6225

Step 4: Round Up the Sample Size

Since we need a whole number for the sample size, we round up: n118 n \approx 118

Final Answer

The required sample size to estimate the population mean height of college basketball players with a 97% 97\% confidence interval and a margin of error of 0.6 0.6 inches is: 118 \boxed{118}

Was this solution helpful?
failed
Unhelpful
failed
Helpful