A manufacturer makes ball bearings that are supposed to have a mean weight of 30 g.

Question

A manufacturer makes ball bearings that are supposed to have a mean weight of 30 g. A retailer suspects that the mean weight is actually greater than 30 g. The mean weight for a random sample of 16 ball bearings is 38.4 g with a standard deviation of 4.5 g. At the 0.05 significance level, test the claim that the sample comes from a population with a mean weight greater than 30 g. Use the traditional method of testing hypotheses.

Answer 1

Hello Kayla! I'm not sure what type of course you're in, but in AP Statistics we're required to complete the 4 Step process of State, Plan, Do, Conclude. I'll provide you with as much of this information as possible. The null is mu = 30 vs alternative of mu >30. Sample mean is 38.4, sample standard deviation is 4.5, and n = 16. Since the population standard deviation is unknown, a t test statistic should be used when doing the significance testing. Due to time constraints, I didn't test the conditions or know whether your class requires the conditions to be tested anyway.

The t test statistic can be calculated by (sample mean - mean from null)/(sample standard deviation/square root of n). Substituting for the variables would be (38.4 - 30)/(4.5/sqr root of 16), which provides a t test statistic of 7.467. To get the p-value, we'd use the tcdf function in your calculator. The parameters are tcdf (7.467, 9999, 15), which provides an extremely small p-value of .000001. The conclusion: Since the p-value (0) is less than alpha (.05), we'd reject the null. There is convincing evidence that the mean weight of the ball bearings exceed 30 grams. Well, I hope that helped Kayla!