Questions: Points: 0.8 of 1 Save The manufacturer of a certain engine treatment claims that if you add their product to your engine, it will be protected from excessive wear. An infomercial claims that a woman drove 3 hours without oil, thanks to the engine treatment. A magazine tested engines in which they added the treatment to the motor oil, ran the engines, drained the oil, and then determined the time until the engines seized. Complete parts (a) and (b) below. (a) Determine the null and alternative hypotheses that the magazine will test.

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The manufacturer of a certain engine treatment claims that if you add their product to your engine, it will be protected from excessive wear. An infomercial claims that a woman drove 3 hours without oil, thanks to the engine treatment. A magazine tested engines in which they added the treatment to the motor oil, ran the engines, drained the oil, and then determined the time until the engines seized. Complete parts (a) and (b) below.
(a) Determine the null and alternative hypotheses that the magazine will test.

Transcript text: Points: 0.8 of 1 Save The manufacturer of a certain engine treatment claims that if you add their product to your engine, it will be protected from excessive wear. An infomercial claims that a woman drove 3 hours without oil, thanks to the engine treatment. A magazine tested engines in which they added the treatment to the motor oil, ran the engines, drained the oil, and then determined the time until the engines seized. Complete parts (a) and (b) below. (a) Determine the null and alternative hypotheses that the magazine will test.

Solution

Solution Steps

Step 1: Define the Null Hypothesis

The null hypothesis (H₀) represents the status quo or the claim being challenged. In this case, the infomercial claims the engine treatment allows a car to run for 3 hours without oil. Therefore, the null hypothesis is that the mean time until engine seizure is equal to 3 hours.

Step 2: Define the Alternative Hypothesis

The alternative hypothesis (H₁) represents what the magazine is trying to prove or disprove. They want to test if the treatment is effective as claimed. The magazine might be skeptical of the 3-hour claim, so their alternative hypothesis is that the mean time until engine seizure is _less than_ 3 hours.