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# (Solved): (a) [3 marks] Explain the distinction between the null and alternative hypotheses. (b) [11 marks] T ...

(a) [3 marks] Explain the distinction between the null and alternative hypotheses. (b) [11 marks] The manufacturer of a new toothpaste claims that at least eight out of ten dentists surveyed prefer their toothpaste and recommend it to their patients. An independent consumer research firm decides to test this claim. The findings in a sample of 400 dentists indicate that do prefer this toothpaste. Is this evidence sufficient to doubt the manufacturer's claim? Use . (c) [11 marks] A professional rock climber claims that he can climb a particular mountain within half an hour. From a random sample of 25 attempts, the rock climber averaged 33.3 minutes with a standard deviation of 3.9 minutes. Is there sufficient evidence to suggest that the climber's claim is incorrect at a significance level of ?

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