ebracch
Answered

Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Our platform offers a seamless experience for finding reliable answers from a network of experienced professionals. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

A U.S. Coast Guard survey of 500 small boats in the Cape Cod area found 195 in violation of one or more
safety regulations.
a. What is the value of the point estimate?
b. What is the critical value you will use for a 95% confidence interval?
C.
What is the value of the standard error?
d. What is the value of the margin of error?
e. State the lower and upper bounds for a 95% confidence interval.
f. State a conclusion, in context.

Sagot :

Using the information given, it is found that:

a) 0.39

b) z = 1.96

c) s = 0.0218

d) M = 0.0428

e)

  • The lower bound is 0.3472.
  • The upper bound is 0.4328.

f) The 95% confidence interval is (0.3472, 0.4328), which means that we are 95% sure that the true proportion of boats who are in violation of one or more  safety regulations is (0.3472, 0.4328).

Item a:

The point estimate is the sample proportion, hence:

[tex]\pi = \frac{195}{500} = 0.39[/tex]

Item b:

95% confidence level, hence [tex]\alpha = 0.95[/tex], the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so [tex]z = 1.96[/tex].

Item c:

The standard error is:

[tex]s = \sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

For this problem, [tex]\pi = 0.39, n = 500[/tex], hence:

[tex]s = \sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]s = \sqrt{\frac{0.39(0.61)}{500}}[/tex]

[tex]s = 0.0218[/tex]

Item d:

The margin of error is:

[tex]M = zs[/tex]

In this problem, [tex]z = 1.96, s = 0.0218[/tex], hence:

[tex]M = zs = 1.96(0.0218) = 0.0428[/tex]

Item e:

The lower bound is:

[tex]\pi - M = 0.39 - 0.0428 = 0.3472[/tex]

The upper bound is:

[tex]\pi + M = 0.39 + 0.0428 = 0.4328[/tex]

The lower bound is 0.3472.

The upper bound is 0.4328.

Item f:

The 95% confidence interval is (0.3472, 0.4328), which means that we are 95% sure that the true proportion of boats who are in violation of one or more  safety regulations is (0.3472, 0.4328).

A similar problem is given at https://brainly.com/question/15136737

Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.