Question

A class survey in a large class for first-year college students asked, "About how many hours do you study during a typical week?" The mean response of the 463 students was x = 15.4 hours. Suppose that we know that the study time follows a Normal distribution with standard deviation σ = 8.9 hours in the population of all first-year students at this university.

(a) Use the survey result to give a 99% confidence interval for the mean study time of all first-year students. (Round your answers to once decimal place.) FILL IN THE BLANKS
______ to _____hours

(b) What condition not yet mentioned must be met for your confidence interval to be valid?

ANSWER A) We need to know if this sample can be considered an SRS of the population of all first-year students at this university.

ANSWER B) We need to know if this sample was a large portion of the population of all first-year students at this university.    

ANSWER C) We need to know if this population is normally distributed.

ANSWER D) We need to know if this sample is normally distributed.

Answer 1

a)

sample mean 'x̄=	15.400
sample size    n=	463.00
std deviation σ=	8.90
std error ='σx=σ/√n=	0.4136

for 99 % CI value of z=		2.576
margin of error E=z*std error =	1.07
lower bound=sample mean-E=	14.3
Upper bound=sample mean+E=	16.5

from above 99% confidence interval for population mean =(14.3 hours to 16.5 hours)

b)

A) We need to know if this sample can be considered an SRS of the population of all first-year students at this university.