Final answer:
To test the claim that most people believe in the Loch Ness monster, we can use a significance level of 0.05 for a hypothesis test. The test result provides strong evidence supporting the claim.
Step-by-step explanation:
To test the claim that most people believe in the Loch Ness monster, we can use a hypothesis test with a significance level of 0.05. The null hypothesis would be that the true proportion of people who believe in the monster is 0.5 (no different from chance), and the alternative hypothesis would be that it is greater than 0.5.
We can set up a z-test using the given data: 61% of 20,738 responses were 'yes.' To find the z-score, we use the formula z = (p - P0) / sqrt((P0 * (1 - P0)) / n), where p is the sample proportion, P0 is the hypothesized proportion, and n is the sample size.
Plugging in the values, we get z = (0.61 - 0.5) / sqrt((0.5 * (1 - 0.5)) / 20738) = 19.44. This z-score is highly unlikely under the null hypothesis, so we reject the null hypothesis and conclude that there is strong evidence to support the claim that most people believe in the Loch Ness monster.
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