A consumer magazine contacted a random sample of 33 owners of a certain car model and asked each owner how many defects had to be corrected within the first 2 months of ownership. The average number of defects was 3.7, with a standard deviation of 1.8 defects. a) Construct a 90% confidence interval for the population mean number of defects for this car model. [2] b) Construct a 95% confidence interval for the population mean number of defects for this car model. [2] c) Construct a 99% confidence interval for the population mean number of defects for this car model. [2] d) Find the length of the confidence intervals. What do you observe about width of the confidence interval as the level of confidence increases?
A consumer magazine contacted a random sample of 33 owners of a certain car model and asked each owner how
many defects had to be corrected within the first 2 months of ownership. The average number of defects was 3.7, with
a standard deviation of 1.8 defects.
a) Construct a 90% confidence interval for the population mean number of defects for this car model. [2]
b) Construct a 95% confidence interval for the population mean number of defects for this car model. [2]
c) Construct a 99% confidence interval for the population mean number of defects for this car model. [2]
d) Find the length of the confidence intervals. What do you observe about width of the confidence interval as the
level of confidence increases?
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