A class survey in a large class for first-year college students asked, \"About h

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 468 students was x = 15.7 hours. Suppose that we know that the study time follows a Normal distribution with standard deviation = 8.1 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.) (b) What condition not yet mentioned must be met for your confidence interval to be valid? a.)We need to know if this sample was a large portion of the population of all first-year students at this university. b.)We need to know if this sample is normally distributed. c.)We need to know if this sample can be considered an SRS of the population of all first-year students at this university. d.)We need to know if this population is normally distributed.

Explanation / Answer

Sol:

n=468

mean=15.7

sd=8.1

z crit for 99%=2.576

99% confidence interval for the mean study time of all first-year students is

samplemean-zcrit*smaplesd/sqrt(n),samplemean+zcrit*smaplesd/sqrt(n)

15.7-2.576(8.1/sqrt(468),15.7+2.576(8.1/sqrt(468)

14.74,16.66

lower limit=14.74

lower limit=14.7

upper limit=16.66

upper limit=16.7(to one decimal)

We are 99% confident that the mean study time of all first-year student lies in between 14.7 and 16.7

Condtitions to be met:

simple random sample

and normal distribution.

Already given sample is form normal distribution.other condition to be met is:

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

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