Question

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.

m=0.29m.SD =0.35m. n=431

a. Identify the population of interest. The mean error of the laser sight Jupiter uses for surveying.

b. Identify the variable of interest. What type of variable is it? The error of each of the 43 measurements. It is Quantitative variable.

c. If she measured the 100m distance BEFORE recalibrating, what would the mean of the measurements have been? The mean would be 0.29m.

d. If she wishes to assess how far off the sight is AFTER recalibrating, what parameter should she estimate? The parameter she should estimate is the difference between the sample mean and population mean error of these 43 measurements after recalibrating.

e. Are the conditions for estimating the parameter you chose in part d met? What assumptions would you need to make? Yes because the assumptions are, The population where the sample is taken should be normally distributed. The population size is at least 10 times the sample size.

f. Estimate the parameter you chose in part d with 99% confidence. Does her recalibration appear to have improved this situation? Sample mean of error= 0.0944 SD= 0.4435 Based on the Z-test, the p-value= 0.0002<0.01, it means the recalibration was effective.

Help with questions below:

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?

Answer 1

a. The population of interest=Measurement of a 100m distance by the laser sight Jupiter before recalibration.

The mean error of the laser sight Jupiter uses for surveying=0.29m

b. The variable of interest=Error of measurement of a 100m distance by the laser sight Jupiter before recalibration. It is Quantitative variable.

c. If she measured the 100m distance BEFORE recalibrating, the mean of the measurements=100+ 0.29=100.29m.

d. Parameter= population mean error measurements after recalibrating.

e. Yes because the assumptions are:

1. the population where the sample is taken should be normally distributed.

2. the population size is at least 10 times the sample size.

f. Sample mean of error= 0.0944, SD= 0.4435.

Based on the Z-test, the p-value= 0.0002<0.01, it means the recalibration was effective.

g. Parameter of interest= population mean error measurements after recalibrating.

h.

Yes because the assumptions are:

1. the population where the sample is taken should be normally distributed.

2. the population size is at least 10 times the sample size.

i.

j. Since the CI contains 0, we are 99% confident that true mean error measurements after recalibrating is not significantly different from zero. Hence we can think that her recalibration made things better.