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)
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)
Solution
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): 3 inches
Margin of error (E): 0.6 inches
Confidence level: 97%
Step 2: Determine the Z-score
For a 97% confidence level, the Z-score (Z) corresponding to the critical value is approximately:
Z≈2.17
Step 3: Calculate the Required Sample Size
Using the formula for the sample size (n):
n=(EZ⋅σ)2
Substituting the known values:
n=(0.62.17⋅3)2
Calculating the numerator:
Z⋅σ=2.17⋅3=6.51
Now, substituting back into the formula:
n=(0.66.51)2=(10.85)2≈117.6225
Step 4: Round Up the Sample Size
Since we need a whole number for the sample size, we round up:
n≈118
Final Answer
The required sample size to estimate the population mean height of college basketball players with a 97% confidence interval and a margin of error of 0.6 inches is:
118