Answer:
a
Step-by-step explanation:
tan = opposite/adjacent
Using an hypothesis test, it is found that:
The p-value of the test is 0.177 > 0.05, which means that there is not significant evidence that the proportion of male goslings is not 50%.
----------------------------
- Test if the proportion of male goslings is different of 50%.
- At the null hypothesis, it is tested if the proportion is of 50%, that is:
![H_0: p = 0.5](https://tex.z-dn.net/?f=H_0%3A%20p%20%3D%200.5)
- At the alternative hypothesis, if is tested if the proportion is different of 50%, that is:
![H_1: p \neq 0.5](https://tex.z-dn.net/?f=H_1%3A%20p%20%5Cneq%200.5)
----------------------------
The test statistic is given by:
![z = \frac{X - p}{\sqrt{\frac{p(1-p)}{n}}}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7BX%20-%20p%7D%7B%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D)
In which
- p is the proportion tested.
- X is the sample proportion.
- n is the size of the sample.
----------------------------
- The proportion tested is 0.5, thus
![p = 0.5](https://tex.z-dn.net/?f=p%20%3D%200.5)
- The sample proportion is 17 out of 27, thus
.
----------------------------
The value of the test statistic is:
![z = \frac{X - p}{\sqrt{\frac{p(1-p)}{n}}}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7BX%20-%20p%7D%7B%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D)
![z = \frac{0.6296 - 0.5}{\sqrt{\frac{0.5\times0.5}{27}}}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7B0.6296%20-%200.5%7D%7B%5Csqrt%7B%5Cfrac%7B0.5%5Ctimes0.5%7D%7B27%7D%7D%7D)
![z = 1.35](https://tex.z-dn.net/?f=z%20%3D%201.35)
----------------------------
- Two-tailed test, thus the p-value of the test is P(|z| > 1.35), which is 2 multiplied by the p-value of z = -1.35.
- Looking at the z-table, z = -1.35 has a p-value of 0.0885.
- The p-value of the test is:
![0.0885 \times 2 = 0.177](https://tex.z-dn.net/?f=0.0885%20%5Ctimes%202%20%3D%200.177)
The p-value of the test is 0.177 > 0.05, which means that there is not significant evidence that the proportion of male goslings is not 50%.
A similar problem is given that brainly.com/question/24166849
Answer: Here is the answer.
Step-by-step explanation: