Chapter 9 Supplemental Homework

1. The laser sight Jupiter uses for surveying is a little off. The mean error is 0.29m, meaning that it tends to provide
measurements that are 0.29m too long. The standard deviation of the errors is 0.35m. She decides to recalibrate the device, but
she wants to test it afterward to see if she made things better or worse. She collects a random sample of 43 measurements of a
100m distance which is found in the data file “surveying.xlsx” on MyLab.

a. Identify the population of interest.
b. Identify the variable of interest. What type of variable is it?
c. If she measured the 100m distance BEFORE recalibrating,what would the mean of the measurements have been?
d. If she wishes to assess how far off the sight is AFTER recalibrating, what parameter should she estimate?
e. Are the conditions for estimating the parameter you chose in part d met? What assumptions would you need to make?
f. Estimate the parameter you chose in part d with 99% confidence. Does her recalibration appear to have improved
this situation?
g. If she wishes to assess how reliable the sight is AFTER recalibrating, what parameter should she estimate?
h. Are the conditions for estimating the parameter you chose in
part g met? What assumptions would you need to make?
i. Estimate the parameter you chose in part g with 99% confidence. Does her recalibration appear to have improved
this situation?
j. Overall, do you think her recalibration made things better or worse?

2. Jupiter is still studying housing insecurity in Avocado Park, and she is particularly concerned with how this is affecting the
children in the neighborhood. To get a sense of the scope of the problem, she selects a random sample of 372 students from
Avocado Park elementary schools and asks them if they have moved more than once in the last 12 months. Forty-two of the
sampled students said that they had.

a. Identify the population of interest.
b. Identify the variable of interest. What type of variable is it?
c. If Jupiter wants to assess how likely members of this population are to face housing insecurity, what parameter
should she estimate?
d. Are the conditions for estimating the parameter you chose in part c met? What assumptions do you need to make?
e. Estimate the parameter you chose in part c with 90% confidence.
f. It is believed that 9% of children in Los Angeles face housing insecurity. How does Avocado Park compare based
on your estimate in part e?
g. If Jupiter wishes to lower her margin of error to 2% while maintaining a 90% level of confidence, how large a sample
would she need?
h. If Jupiter wishes to lower her margin of error to 2% while maintaining a 90% level of confidence but she doesn’t trust
the results of her previous survey, how large a sample could she possibly need?