Question

A washing machine manufacturing company claims that an average washing machine lasts 300 days. A researcher randomly selects 15 machines for testing. The sample machines last an average of 290 days with a standard deviation of 50 days. If the company's claim is true, find the range of probability (area in right tail from the table) that 15 randomly selected machines would have an average life of no more than 290 days, in other words where does your t-statistic lie in the table?

(Use the formula for t-distribution, to compute the t-statistic, the replacement of z-score here.)

Answer 1

Solution:

Given: A washing machine manufacturing company claims that an average washing machine lasts 300 days.

That is:

Sample size = n = 15

Sample mean =

Sample standard deviation = s = 50

We have to find the range of probability that 15 randomly selected machines would have an average life of no more than 290 days .

Thus find t test statistic:

To find range of probability that 15 randomly selected machines would have an average life of no more than 290 days , that is to find the range of probability that t < -0.775 , we look in t table for df = n - 1 = 15 -1 = 14 row and look in that row for absolute t = 0.775

thus find an interval in which t = 0.775 fall and then find corresponding one tail area.

this range of one tail area gives range of probability for t > 0.775

that also means range of probability for t < - 0.775

Thus we get:

absolute t = 0.775 fall in between 0.692 and 0.868

corresponding one tail area is between 0.20 and 0.25

Thus range of probability that 15 randomly selected machines would have an average life of no more than 290 days is between 0.20 and 0.25