A researcher wanted to determine if carpeted or uncarpeted rooms contain more bacteria. The table shows the number of bacteria per cubic foot for random samples of both types of rooms.

Test whether the median amount of bacteria in carpeted rooms was greater than the median amount of bacteria in uncarpeted rooms at the \(\alpha=0.05\) level of significance.

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Carpeted Uncarpeted 9 9.8 8.2 8.2 6.9 7 9.9 8 10 10.2 10.1 7 8.1 6.5 7.2 6.6