A travel agency is interested in finding out if different age groups frequent different Spring Break destinations, in order to better target the appropriate audiences. A random sarfhple of college Spring Break vacationers produces the results given in the table below. Is there enough evidence at the 0.005 level of significance to show that there is a relationship between age (by college classification) and destination?
\begin{tabular}{|c|c|c|c|c|c|}
\hline \multicolumn{7}{|c|}{ Observed Sample of College Students } \\
\hline & Beach & Mountains & City & Home & Total \\
\hline Freshman & 21 & 12 & 2 & 19 & 54 \\
\hline Sophomore & 26 & 16 & 22 & 23 & 87 \\
\hline Junior & 22 & 9 & 2 & 18 & 51 \\
\hline Senior & 18 & 7 & 9 & 13 & 47 \\
\hline Total & 87 & 44 & 35 & 73 & 239 \\
\hline
\end{tabular}
Copy Data
Step 1 of 4: Calculate the expected value for the number of freshmen going to the beach during Spring Break. Round your answer to six decimal places.
Answer
Thus, the expected value for the number of freshmen going to the beach during Spring Break is \(\boxed{19.656904}\).
Step 1 ：Given the total number of freshmen is 54, the total number of students going to the beach is 87, and the total number of students is 239.
Step 2 ：The expected value can be calculated by multiplying the row total by the column total and then dividing by the grand total.
Step 3 ：Using the formula \(\frac{{row\_total \times column\_total}}{{grand\_total}}\), we substitute the given values to get \(\frac{{54 \times 87}}{{239}}\).
Step 4 ：Calculating the above expression, we get an expected value of approximately 19.656903765690377.
Step 5 ：Rounding this to six decimal places, we get 19.656904.
Step 6 ：Thus, the expected value for the number of freshmen going to the beach during Spring Break is \(\boxed{19.656904}\).
