23 A study was done to find out how long on average it takes

23

A study was done to find out how long on average it takes Franklin students in a college level math class to complete the weekly assignments. A simple random sample of 32 students was taken and the average time in hours to complete their weekly math assignments is recorded in the table below.

a. What is the point estimate for the mean of all assignment times?

b. Construct a 90% confidence interval for the mean amount of times it takes to complete the weekly assignments in this math class. (Show your formula set up or your calculator command.)

c. What is the margin of error?

d. List two ways to make this margin of error smaller.

e. Interpret the confidence interval you got in part b in the context of the problem. Use complete sentences.

4.2 1.8 3.6 2.25.3 7.4 6.4 3.5 2.9 4.6 3.95 4.8 3.8 2.8 6.4 3.2 2.75.3 6.04.6 4.9 4.1 3.8 5.2 6.6 7.8 2.5 3.7 1.9 2.0 4.5 5216.6-i78- 2.5 13.7 11.9 12.0

Solution

a. What is the point estimate for the mean of all assignment times?

point estimate= 4.296875

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b. Construct a 90% confidence interval for the mean amount of times it takes to complete the weekly assignments in this math class. (Show your formula set up or your calculator command.)

Given a=1-0.9=0.1, Z(0.05) = 1.645 (from standard normal table)

The sample standard deviation =1.588971

So the lower bound is

xbar - Z*s/vn =4.296875 -1.645*1.588971/sqrt(32) =3.834806

So the upper bound is

xbar + Z*s/vn =4.296875 +1.645*1.588971/sqrt(32) =4.758944

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c. What is the margin of error?

The margin of error =Z*s/vn

=1.645*1.588971/sqrt(32)

=0.4620691

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d. List two ways to make this margin of error smaller.

Increase sample size

Decrease the confidence interval level

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e. Interpret the confidence interval you got in part b in the context of the problem. Use complete sentences.

We have 90% confident that the population mean amount of times it takes to complete the weekly assignments in this math class will be within this interval.