n the paper "Persistent Pulmonary Hypertension of the Neonate and Asymmetric Growth

Restriction" (

obstetrics & Gynecology

, Vol. 91, No. 3, pp. 336

-

341

, 2000

), M. Williams et

al. reported on a study of characteristics of neonates. Infants treated for pulmonary

hypertension, called the PH group, were compared with those not so treated, cal

led the

control group. One of the characteristics measured was head circumference. The mean

head circumference of the 10 infants in the PH group was 34.2 centimeters (cm).

 

Required:

 

a)

Assuming that head circumferences for infants treated for pulmonary hypertension

are normally distributed (symmetrical) with a population standard deviation of 2.1

cm. Determine a 90% confidence interval for the mean head circumference of all

such infants.

Provide a statement for your answer.

(5 marks)

 

b)

What are the two basic statistical assumptions to validate the confidence interval

result of part (a) above?

(2

m

arks)

 

c

)

Obtain the margin of error,

E

, for the confidence interval you found in part (a) above.

(

2

mark

s

)

 

d

)

Explain the meaning of

E

in this content in terms of the accuracy of the estimate.

(

2

mark

s

)

 

e

)

Determine the sample size required to have a margin of e

rror,

E

, of 0.5 cm with a

90% confidence level. Provide a statement.

(

4

marks)

a) Lower limit = ?μ? - E = 34.2 - 1.217256 = 32.98274

Upper limit = ?μ? + E = 34.2 + 1.217256 = 35.41726

b)

1. Randomization Assumption: The data must be sampled randomly.
2. Independence Assumption: The sample values must be independent of each other. 
3. Sample Size Condition: The sample size must be sufficiently large. here sample size <30 

c)

E = 1.217256

d)he margin of error is a statistic expressing the amount of random sampling error in the results of a survey. 

A margin of error tells you how many percentage points your results will differ from the real population value.

e) sample size n = 59

Step-by-step explanation

Given information is

Population mean ?μ? = 34.2 centimeters 

population standard deviation ?σ? = 2.1 cm

sample size n =10

we have to calculate 90% confidence interval for the mean head circumference of all such infants.

a) formula for 90% confidence interval for the mean

?μ? +- E -----------------where E is margin of error

Now calculate E ( sample size < 30 so, we use t critical value with 9 df)

E = t* ?n?σ??

E = 1.833 * ?1?02.1??

E = 1.217256

Lower limit = ?μ? - E = 34.2 - 1.217256 = 32.98274

Upper limit = ?μ? + E = 34.2 + 1.217256 = 35.41726

b)

1. Randomization Assumption: The data must be sampled randomly.
2. Independence Assumption: The sample values must be independent of each other. 
3. Sample Size Condition: The sample size must be sufficiently large. here sample size <30 

c) Now calculate margin of error E

E = t* ?n?σ??

E = 1.833 * ?1?02.1??

E = 1.217256

d)The margin of error is a statistic expressing the amount of random sampling error in the results of a survey. 

A margin of error tells you how many percentage points your results will differ from the real population value.

e)Determine the sample size required to have a margin of error,E=0.5 cm with a 90% confidence level.

we know formula for calculating margin of error

E = t* ?n?σ??

0.5 = 1.833 * ?n?2.1??

?n?? = (1.833 *2.1 )/0.5

?n?? = 7.6986

n = 59.26844 ------------squaring on both side

sample size n = 59