Respuesta :
Answer:
The 95% confidence interval for the population proportion of people who believe the governor broke campaign financing laws is (33%, 39%).
Step-by-step explanation:
The (1 - α) % confidence interval for population proportion is:
[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
For a 95% confidence interval the critical value of z is:
[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96[/tex]
The sample proportion is, [tex]\hat p =0.36[/tex] and the sample size is, n = 900.
Compute the 95% confidence interval for the population proportion of people who believe the governor broke campaign financing laws as follows:
[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.36\pm 1.96\times\sqrt{\frac{0.36(1-0.36)}{900}}\\=0.36\pm0.03136\\=(0.32864, 0.39136)\\\approx(0.33, 0.39)[/tex]
The 95% confidence interval for the population proportion of people who believe the governor broke campaign financing laws is (33%, 39%).
The null hypothesis can be defined as:
H₀: More than 38% of all U.S. citizens favor that viewpoint, i.e. p > 0.38.
As the 95% confidence interval consists of the null value so it can concluded that fewer than 38% of all U.S. citizens favor that viewpoint.
