confidence intervals for proportions take home test

8/9/2019 Confidence Intervals for Proportions Take Home Test

1/5

Name:_______________________________________ Date:______ Period:______

Score:___/43

AP Statistics Take Home Exam: Confdence Intervas !or Pro"ortions #$"en Ended: 33

"oints%

1. In 2002 the medical journal The Lancet reported that 335 of 573 patients suering from

Crohn’s disease responded positivel to injections of the arthritis!"ghting drug in#i$ima%.

a. &etermine if it appropriate to create a one!proportion '!interval for this data. ()points*

%. Calculate a +,- con"dence interval for the proportion of Crohn’s patients ho

responded positivel to injections of in#i$ima%. /ho all appropriate or or. (points*

c. Interpret the meaning of this interval in conte$t. ( points*

d. If e decreased the level of con"dence to +0-... (2 points*

i. o ould the idth of the interval %e aected4

ii. o ould the margin of error %e aected4

e. If e increased the sample si'e (2 points*

i. o ould the idth of the interval %e aected4

ii. o ould the margin of error %e aected4


2/5

f. 6nother medical stud plans to estimate the percentage of Crohn’s patients ho

respond positivel to in#i$ima% to ithin - ith +5- con"dence. hat is a

conservative estimate (assume p!hat is 0.5* for the num%er of students he should

sample4 (3 points*

2. 6 statistics professor at a local universit ased her students hether or not the ere

registered to vote. In a sample of 50 of her students (randoml sampled from her 700

students* 70- said the ere registered to vote.a. 8stimate the true proportion9percentage of students (at this college* ho are

registered to vote (ith +0- con"dence*. 6ssume the conditions for inference have

%een satis"ed. /ho an appropriate or in the space %elo. ( points*

%. 8$plain the meaning of :+0- con"dence; in this conte$t. (3 points*

c. 6ccording to a universit ohe resulting interval as (,.- 57.211-*. ?ind

the value of p!hat and the margin of error for this interval. (2 points*


3/5

1. Which of the following statements best describes the relationship between a parameter and a statistic?

A. A parameter has a sampling distribution with the statistic as its mean.

B. A parameter has a sampling distribution that can be used to determine what values the statistic is likely to have in

repeated samples.

C. A parameter is used to estimate a statistic.

D. A statistic is used to estimate a parameter.

2. Which of the following statements is correct about a parameter and a statistic associated with repeated random

samples of the same size from the same population?

A. Values of a parameter will vary from sample to sample but values of a statistic will not.

B. Values of both a parameter and a statistic may vary from sample to sample.

C. Values of a parameter will vary according to the sampling distribution for that parameter.

D. Values of a statistic will vary according to the sampling distribution for that statistic.

3. Five hundred (5! random samples of size n"# are ta$en from a large population in which 1% are left&handed.

'he proportion of the sample that is left&handed is found for each sample and a histogram of these 5 proportions is

drawn. Which interval covers the range into which about )% of the values in the histogram will fall?

A. .1 @ .010

B. .1 @ .01!

C. .1 @ .01"#

D. .1 @ .0$0

*. + randoml, selected sample of * students at a universit, with 15&wee$ semesters was as$ed whether or not the, thin$

the semester should be shortened to 1* wee$s (with longer classes!. Fort,si- percent (*%! of the * students surve,ed

answered ,es. Which one of the following statements about the number *% is correct?

A. %t is a sample statistic.

B. %t is a population parameter.

C. %t is a margin of error.

D. %t is a standard error.

5. + poll is done to estimate the proportion of adult +mericans who li$e their /obs. 'he poll is based on a random sample

of * individuals. What is the 0conservative margin of error of this poll for a #5% confidence interval?

A. 0.10 B. 0.0& C. 0.0! D. 0.0$&


4/5

. When constructing a onfidence nterval4 which case is preferable?

• A& large con"dence level small con"dence interval

• '& small con"dence level small con"dence interval

• C& small con"dence level large con"dence interval

• D& large con"dence level large con"dence interval

. Which of the following is 67' a point estimate (estimate of a single value?

• A& $!%ar

• '& p!hat or p!prime

• C& /$

• D& sigma

). + stud, was done to determine the proportion of voters that feel that their local government is doing an

ade8uate /ob. 7f the 1 voters surve,ed4 1** feel that their local government is doing an ade8uate /ob.

alculate the #5% confidence interval for the true proportion of voters that feel that their government is doing

an ade8uate /ob.

• A& (0.,5 0.+5*

• '& 0.+0

• C& (0.,0 1.00*

• D& (1 1)0*

#. 'o reduce the margin of error in a future stud,4 which of the following should be done?

• A& increase the sample si'e n

• '& decrease the sample si'e n

• C& conduct a %iased surve

• D& increase the con"dence level

10. 1,600 of 2,000 voters say they plan to vote Republican. Use 0.95 deree of con!dence to

!nd the population proportion interval.

6. )+.2 to ,).-

=. 7).5 to ,3.5-

C. 77.7 to ,2.3-

&. 7,.2 to ,1.,-

8. none of the a%ove


5/5

confidence intervals for proportions take home test

Documents