A consumer is frustrated, because even though his toothpaste tube is advertised

Question

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 hypoth- esis test procedure to determine if the consumer has grounds to sue the toothpaste manufacturer 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 hypoth- esis test procedure to determine if the consumer has grounds to sue the toothpaste manufacturer 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 hypoth- esis test procedure to determine if the consumer has grounds to sue the toothpaste manufacturer 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 hypoth- esis test procedure to determine if the consumer has grounds to sue the toothpaste manufacturer

Explanation / Answer

Step: 1 Assumptions and Hypothesis :

(a) Here the distribution of toothpaste weight is normal.

(b) Random sampling has been done.

Null hypothesis : H0 : The unusable amount is less than equal to 10% of the toothpaste he pays for. <= 0.5 oz

Alternative Hypothesis : Ha : The unusable amount is more than 10% of the toothpaste he pays for. > 0.5 oz

Step :II Calculate appropriate test statistic : t- test will be aprropriate.

xbar = 0.502 oz and s = 0.1023 oz

t = (xbar - h)/ (s/n) = (0.502 - 0.5)/ (0.1023/5) = 0.002/ 0.0457 = 0.0438

Step : III Identify critical values of test and p - value

For dF = 4 and alpha = 0.05 , tcritical = 2.138

P - value = 0.9672

Step : IV Reject or accept Null Hypothesis

As the P - value is not under significance level, we cannot reject the null hypothesis.

Step :V Conclusion

Here, We can conclude that consumer doesn't have grounds to sue the toothpaste manufacturer.

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