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Sagot :
Using the z-distribution, it is found that since the test statistic is less than the critical value for the right-tailed test, it is found that it can be concluded that the proportion of the population in favor of candidate A is not significantly greater than 0.75.
At the null hypothesis, it is tested if the proportion is not significantly more than 75%, that is:
[tex]H_0: p \leq 0.75[/tex]
At the alternative hypothesis, it is tested if the proportion is significantly more than 75%, that is:
[tex]H_1: p > 0.75[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
- [tex]\overline{p}[/tex] is the sample proportion.
- p is the proportion tested at the null hypothesis.
- n is the sample size.
In the sample, 80 out of 100 people favored candidate A, hence, the parameters are:
[tex]n = 100, \overline{p} = \frac{80}{100} = 0.8, p = 0.75[/tex]
Hence:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.8 - 0.75}{\sqrt{\frac{0.75(0.25)}{100}}}[/tex]
[tex]z = 1.15[/tex]
The critical value for a right-tailed test, as we are testing if the proportion is greater than a value, is [tex]z^{\ast} = 1.645[/tex].
Since the test statistic is less than the critical value for the right-tailed test, it is found that it can be concluded that the proportion of the population in favor of candidate A is not significantly greater than 0.75.
To learn more about the use of the z-distribution to test an hypothesis, you can take a look at https://brainly.com/question/25584945
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