A consumer magazine has contacted a simple random sample of 33 owners of a certain model of automobile and asked each owner how many defects had to be corrected with in the first 2 months of ownership. The average number of defects was x with (with line over the x)=3.7, with a standard deviation of 1.8 defects.

Question

a. Use the t distrubution to construct a 95% confidence interval for u = the average number of defects for this model.

b. Use the z distrubution to construct 95% confidence interval for u = the average number of defects for this model.

c. Given that the population standard deviation is not known, which of these two confidence intervals should be used as the interval estimate for u?

Answer 1

Use confidence interval formulas to construct the interval for µ.

CI95 = mean + or - 1.96 (sd/√n)
...where + or - 1.96 represents the 95% interval using a z-distribution, sd = standard deviation, and n = sample size.

Confidence interval using a t-distribution would be the same EXCEPT you will need to look at a t-table using degrees of freedom (which is n-1) for the + or - value.

You should be able to determine which confidence interval should be used.

I hope this will help get you started.

Answer 2

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