Recently the cost of guarantees has increased considerably. It has been decided
ID: 3321806 • Letter: R
Question
Recently the cost of guarantees has increased considerably. It has been decided to evaluate if the average of the "shelf life" has been maintained in 20 months or if it has decreased, thus increasing the cost by way of customer claims.
to. What kind of test would you do?
b. If the reduction in the average shelf life is 1 month or more, you want the test to have a 90% probability of detecting the decrease. If it is known that the standard deviation in shelf life is 0.75 months, what sample size should we use?
Use the data provided to determine if the average shelf life has changed.
1. Clearly establish the test you will perform
2. Establish any presumption necessary
3. Carry out the computations
4. Report your conclusion in complete sentences and in keeping with the situation
Data:
20.0497 18.5835 20.8664 22.4147 22.2975 23.0997 17.2246 20.1487 22.1425 18.8699 19.4647 17.9644 17.7296 19.0336 19.3397 17.3231 19.6481 19.8939 20.7023 19.9518 20.0095 19.9446 22.5140 20.3721 20.2208 19.7302 23.4583 21.7985 24.0635 19.5176 22.9922 18.0814 21.3084 21.8533 23.3784 20.3732 19.7143 21.5127 19.9280 21.6364Explanation / Answer
a)
sample mean(xbar) = 20.48
Sample standard deviaiton (s) = 1.751
H0 : u = 20
H1 : u 20
Decision rule : If T statistic < -2.023 then reject H0
T statistic = xbar - µ /(s/n)
= 20.48 - 20 / [1.751/sqrt(40)] = 1.733
Here T statistic > -2.022, So fail to reject H0
we conclude that there is no sufficient evidence that the true mean is less than 20
b) sample size 'n' = (z critical * sd / margin error)2 = (1.645 * 0.75 / 1)2 = 5
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