The gym is looking for a new equipment supplier. The candidate manufacturer provided for the equivalence...

The gym is looking for a new equipment supplier. The candidate manufacturer provided for the equivalence testing a set of ten dumbbells with a nominal weight of 12-kg. The sample mean and sample standard deviation of the weight of these sample dumbbells are 12.06-kg and 0.06-kg, respectively. The gym is going to sign a contract if the mean weight of a dumbbell is within 0.05-kg of the nominal weight. Would you recommend the gym to sign a contract with this manufacturer?

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Expert Solution

The allowable limit for the the mean weight of a dumbbell = 12 +/- 0.04 = 11.95 to 12.05

For testing the manufacturer's claim, we will calculate 95% confidence interval.

Based on sample data, the 95% confidence interval shows that true mean weight of a dumbbell can also exceed the 12.05. This is because upper limit of confidence interval (12.103) is greater than 12.05. Thus, I would not recommend the gym to sign a contract with this manufacturer.

orchestra answered 1 year ago

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