Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
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
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.
