Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
Answer:
The 95% confidence interval for the true proportion of businesses owned by women is (0.2763, 0.4037).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
A survey of businesses in a particular state found that out of 150 surveyed, 51 were owned by women.
This means that [tex]n = 150, \pi = \frac{51}{150} = 0.34[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.34 - 1.96\sqrt{\frac{0.34*0.66}{150}} = 0.2763[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.34 + 1.96\sqrt{\frac{0.34*0.66}{150}} = 0.4037[/tex]
The 95% confidence interval for the true proportion of businesses owned by women is (0.2763, 0.4037).
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
