The Arcade shack is a manufacturing plant located in San Diego where 800 factory workers are employed. The personnel department selected 36 factory employees at random for the statistical study. construct a 95% interval for the percentage of males in the 800.
To construct a confidence interval for the percentage of males in the 800 factory workers, you can follow these steps:
Step 1: Define the sample proportion
First, you need to find the proportion of males in the sample of 36 factory employees. Let's say the number of male employees in the sample is x, so the sample proportion of males (p̂) is x/36.
Step 2: Calculate the standard error
The standard error (SE) measures the variability of the sample proportion. In this case, since the sample size is sufficiently large (n = 36), we can approximate the standard error using the formula:
SE = √[(p̂ * (1 - p̂)) / n].
Step 3: Determine the margin of error
The margin of error quantifies the variability around the sample proportion. To calculate it, you need to know the critical value corresponding to the desired confidence level. For a 95% confidence level, the critical value is 1.96.
Margin of Error = Critical Value * Standard Error
Step 4: Calculate the confidence interval
The confidence interval is determined by subtracting and adding the margin of error to the sample proportion.
Lower Limit = Sample Proportion - Margin of Error
Upper Limit = Sample Proportion + Margin of Error
Now, let's plug in the values to obtain the confidence interval:
Sample Proportion = x/36
Standard Error = √[(p̂ * (1 - p̂)) / n]
Margin of Error = 1.96 * Standard Error
Lower Limit = Sample Proportion - Margin of Error
Upper Limit = Sample Proportion + Margin of Error
Note: Since you haven't provided the number of male employees in the sample, it is not possible to give you a specific confidence interval. But now you have the steps needed to calculate it once you have the necessary information.