Let's evaluate each statement:
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True - The user's first hypothesis was that the lamp wire was unplugged, and they tested that hypothesis by confirming that the wire was firmly plugged into the outlet.
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True - The user's second hypothesis was that the bulb was broken, and they tested that hypothesis by shaking the bulb and listening for rattling, which is a common method to check for a broken filament in incandescent bulbs.
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True - The user's third hypothesis was that the outlet was dead, and they tested that hypothesis by plugging a known-working lamp into the outlet, which is a valid method to check if the outlet is functioning properly.
Overall, all three statements are true.