Question

Suppose 250 randomly selected students in a college are surveyed to determine if they own a tablet. Of the 250 surveyed, 98 reported owning a tablet.

a. explain whether normal model can be used in this situation

b. find the standard error.

c. Construct the 95% confidence interval and explain what it means in the context of the problem

d. based on the college database, the proportion of students that owns a tablet in this college is 36% What is the probability, that a sample of 250 random selected students, more than 100 owns a tablet?

Answer 1

a)

here since number of success =98 and number of failure =250-98=152 , both are greater than 10,

we can use normal approximation of binomial distribution

b)

sample proportion p̂ =x/n=		0.3920
std error se= √(p*(1-p)/n) =√(0.392*(1-0.392)/250) =		0.0309

c)

for 95 % CI value of z=		1.96
margin of error E=z*std error   =		0.0605
lower bound=p̂ -E                       =		0.331
Upper bound=p̂ +E                     =		0.453
from above 95% confidence interval for population proportion =(0.331,0.453)

above interval gives 95% confidence to contain true value of population proportion

d)

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.360
sample size       =n=	250
std error of proportion=σp=√(p*(1-p)/n)=	0.0304

probability, that a sample of 250 random selected students, more than 100 owns a tablet or

more than (100/250 =0.40 proportion):

probability =P(X>0.4)=P(Z>(0.4-0.36)/0.03)=P(Z>1.32)=1-P(Z<1.32)=1-0.9066=0.0934