Using the z-distribution, since the p-value of the test is less than 0.01, there is enough evidence to conclude that the claim is correct.
<h3>What are the hypothesis tested?</h3>
At the null hypothesis, it is tested if there is not enough evidence that the proportion is above 0.5, hence:
At the alternative hypothesis, it is tested if there is enough evidence that the proportion is above 0.5, hence:
<h3>What is the test statistic?</h3>
The test statistic is given by:
In which:
- is the sample proportion.
- p is the proportion tested at the null hypothesis.
For this problem, the parameters are:
Hence the test statistic is:
z = 6.1.
<h3>What is the p-value?</h3>
We have a right-tailed test, as we are testing if the proportion is greater than a value. Using a z-distribution calculator, with z = 6.1, the p-value is of 0.
Since the p-value is less than 0.01, there is enough evidence to conclude that the claim is correct.
More can be learned about the z-distribution at brainly.com/question/16313918
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