Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
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
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.
