4. A consumer is frustrated, because even though his toothpaste tube is advertis

Question

4. A consumer is frustrated, because even though his toothpaste tube is advertised to contain 5oz of toothpaste he does not seem able to squeeze all of the toothpaste out of the tube. He randomly selects 5 tubes of the same brand of toothpaste and squeezes each until he can’t get any more toothpaste out. Then he cuts open each tube, removes the remaining toothpaste and weighs it.

His measurements are 0.53, 0.65, 0.46, 0.5, 0.37 oz, respectively.

His attorney informs him that he would have a reasonable case to sue the toothpaste manufacturer if he could demonstrate that more than 10% of the toothpaste he pays for is not useable (because it can’t be squeezed out of the tube). Assuming that the distribution of remaining toothpaste weight is Normal and that the population standard deviation is known to be 0.15oz, conduct a 5-step hypothesis test procedure to determine if the consumer has grounds to sue the toothpaste manufacturer.

Explanation / Answer

10% of the toothpaste is .1*5oz = 0.5oz.

Mean, x = (0.53+0.65+0.46+0.5+0.37)/5 = 0.502

= 0.15oz

Ho, µ <= 0.5
Ha: µ > 0.5

One sample one tailed z test.

test statistic: z = (0.502 - 0.5)/0.15 = 0.013333

significance level, = 0.05

p = 0.4947 > 0.05, fail to reject the null hypothesis, there is insufficient evidence to conclude the consumer has grounds to sue the toothpaste manufacturer.

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