Question

Park rangers are analyzing the proportion of raccoons that are infected with distemper virus in a park. The rangers sampled 125 raccoons using a catch and release protocol. 8 of the raccoons had distemper virus in them. Obtain a confidence interval for the proportion of raccoons that are infected with distemper virus in the park. Use ? = 0.01.

What is the population? A. Raccoons in the park

B. The park

C. Raccoons infected with distemper virus

D. Raccoons with infections in the park

E. Raccoons

What is the parameter?

A. Number of raccoons in the park

B. Proportion of raccoons infected with a virus in the park

C. Number of raccoons infected with a virus in the park

D. Proportion of raccoons in the park

E. Proportion of raccoons infected with distemper virus in the park

What is the statistic?

What is the standard error for the proportion?

What is the critical value?

What is the margin of error?

What is the confidence interval for the population proportion?

How many raccoons should be caught and released for a study that requires a 1.69% of error at the same level of significance?

Identify the true statement.

I. If 536 are observed in the park, at least 4 of them are likely to be infected with distemper virus with 99% certainty.

II. If 536 are observed in the park, at most 65 of them are likely to be infected with distemper virus with 1% certainty.

III. If 536 are observed in the park, at least 4 of them are likely to be infected with distemper virus with 1% certainty.

IV If 536 are observed in the park, at least 65 of them are likely to be infected with distemper virus with 99% certainty.

A. I and II only

B. IV only

C. I only

D. III and IV only

E. I and IV only

Answer 1

Population refers to the total number of observation that can be made. As here we are finding raccoons that are infected with distemper virus in a park.

So Population is C. Raccoons infected with distemper virus

Parameter means which tells us something about the whole population so here parameter is

B. Proportion of raccoons infected with a virus in the park.

Statistics is the value of interest but from sample

Here n=125 and x=8, so statistics is

Standard error is

Here , So CI is

Hence z value for 99% CI is 2.58 as

So Margin of Error is

Hence CI is