13. A television manufacturer takes a random sample of 30 customers and determines the times (after...

13.

A television manufacturer takes a random sample of 30 customers and determines the times (after purchasing) until the televisions need servicing have a mean of 6 years and a standard deviation of 1.2 years.

a) Determine the 95% confidence interval for the mean and explain whether it is reasonable for the company to claim the mean time until servicing is needed is 6.4 years.

b) Repeat a), but use a 90% interval.

c) Suppose instead a larger sample of 100 customers was taken and it had the same mean and standard deviation as the sample of 30. Determine both the 90% and 95% confidence intervals. Does either interval support the company’s claim that the mean time is 6.4 years until servicing is needed?

Solutions

Expert Solution

( a )

yes , it is reasonable for the company to claim the mean time until servicing is needed is 6.4 years. because

6.4 lies between 5.552 and 6.448

( b )

No , it is not reasonable for the company to claim the mean time until servicing is needed is 6.4 years. because

6.4 does not lies between 5.628 ad 6.372

( c )

No , it is not reasonable for the company to claim the mean time until servicing is needed is 6.4 years. because

6.4 does not lies between 5.762 and 6.238

No , it is not reasonable for the company to claim the mean time until servicing is needed is 6.4 years. because

6.4 does not lies between 5.801 and 6.199

orchestra answered 1 year ago

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