Suppose a random sample of 888 adults from your town are surveyed. The table below shows the results of the survey. Observed Frequencies Job Types the Sample \begin{tabular}{|l|l|} \hline \multicolumn{1}{|c|}{ Outcome } & Observed Frequency \\ \hline Blue Collar & 213 \\ \hline White Collar & 293 \\ \hline Pink Collar & 338 \\ \hline Unemployed & 44 \\ \hline \end{tabular} The job type distribution for the entire state are summarized in second column of the table below. Fill in the expected frequencies. Frequencies of Job Types in the State \begin{tabular}{|c|c|c|} \hline Outcome & \begin{tabular}{c} Expected \\ Percent \end{tabular} & Expected Frequency \\ \hline Blue Collar & 21 & \\ \hline White Collar & 27 & \\ \hline Pink Collar & 46 & \\ \hline Unemployed & 6 & \\ \hline \end{tabular} Hint: Helpful Video [ [+]
Solution
Step 1 ：The problem provides the job type distribution for the entire state and a random sample of 888 adults from your town. The task is to calculate the expected frequencies of each job type in the sample.
Step 2 ：The expected frequency for each job type can be calculated by multiplying the total sample size by the expected percent for each job type.
Step 3 ：For example, the expected frequency for Blue Collar jobs can be calculated as follows: Expected Frequency (Blue Collar) = Total Sample Size * Expected Percent (Blue Collar). This calculation needs to be done for each job type.
Step 4 ：Let's calculate the expected frequencies for each job type: \n Blue Collar: \(888 * 0.21 = 186.48\) \n White Collar: \(888 * 0.27 = 239.76\) \n Pink Collar: \(888 * 0.46 = 408.48\) \n Unemployed: \(888 * 0.06 = 53.28\)
Step 5 ：The expected frequencies for each job type are approximately as follows: \n Blue Collar: \(\boxed{186.48}\) \n White Collar: \(\boxed{239.76}\) \n Pink Collar: \(\boxed{408.48}\) \n Unemployed: \(\boxed{53.28}\)
