Final answer:
Based on the confidence interval and the machine's specification range, there is no convincing evidence that the machine is malfunctioning.
Step-by-step explanation:
Based on the information provided, we are given the following:
- Best estimate of the population mean displacement is 0.2 cm
- Best estimate of the population standard deviation is 0.3 cm
- Best estimate of the standard error of the sample mean displacement is 0.4 cm
- Lower bound of a 95% confidence interval for the mean displacement is 0.5 cm
- Upper bound of a 95% confidence interval for the mean displacement is 0.6 cm
- The machine's specifications state that the average displacement may be as large as 0.95 cm
To determine if there is convincing evidence that the machine is malfunctioning, we need to consider if the true population mean displacement falls within the machine's specification range. Since the upper bound of the 95% confidence interval for the mean displacement is 0.6 cm and it is smaller than the machine's specification of 0.95 cm, there is no convincing evidence that the machine is malfunctioning. The measured displacements are within the acceptable range.
The complete question is:
You own a firm which places logos on jerseys, and you have grown suspicious that one of your logo machines is not centering the logo properly. You commission a study to measure how far (in centimeters) from "dead center" the average logo is being placed by this machine.
A simple random sample of jerseys is selected for study; the displacement (in centimeters) of the logo from "dead center" on each jersey in the sample is accurately measured and recorded in a data file named Jerseys.txt. Each record in this file corresponds to one jersey, and the displacement (in centimeters) of the jersey's logo has been recorded in columns 1-5. (Note that this number cannot be negative.)
Based on these data, and using only Excel, please answer the following questions:
1. The best estimate of the population mean displacement is .
2. The best estimate of the population standard deviation of the displacement is .
3. The best estimate of the standard error of the sample mean displacement is .
4. The lower bound of a 95% confidence interval for the mean displacement (based on the Empirical Rule) is .
5. The upper bound of a 95% confidence interval for the mean displacement (based on the Empirical Rule) is .
6. If the machine's specifications say that the average displacement may be as large as .95cm, is there convincing evidence that the machine is malfunctioning? (No/Yes) Why/Why not?