Have you ever been frustrated because you could not get a container of some prod

Question

Have you ever been frustrated because you could not get a container of some product to release the last bit of its contents (make-up, toothpaste, lotion etc)? The article “Shake, rattle and Sqeeze: How Much is Left in That Container? “ (Consumers Reports, May 2009: 8) reported on an investigation of this issue for various consumer products. Suppose nine tubes of toothpaste, of the same brand and size (6 oz), are randomly selected and squeezed until no more toothpaste will come out. Then each tube is cut open and the amount remaining is weighed, resulting in an average amount remaining of 0.57 oz and sample standard deviation of 0.03 oz. Is there evidence that the true average amount left in the bottle is less than 0.60 oz, which is less than 10% of the advertised weight? Assume the population to be normally distributed. Use a significance level of 0.05.

State: Is there evidence that the true average amount left in the bottle is less than 0.60 oz, that is, less than 10% of the advertised weight?

Plan:

   a. (2 points) State the null and alternative hypotheses to answer the question of interest.

b. (2 points) What type of test is appropriate to answer the question of interest and why?

Explanation / Answer

a. H0:mu greaer than equal to 0.60 (The true amount left in bottle is greater than or equal to 0.60 oz)

H1:mu < 0.60 (The true amount left in bottle is less than 0.60 oz).

b. The population standard deviation is unknown and sample size , 9 is less than 30, use 1 sample-t test.

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