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Solved: Have you ever been frustrated because you could
Chapter 8, Problem 36E(choose chapter or problem)
Have you ever been frustrated because you could not get a container of some sort to release the last bit of its contents? The article “Shake, Rattle, and Squeeze: How Much Is Left in That Container?” (Consumer Reports, May 2009: 8) reported on an investigation of this issue for various consumer products. Suppose five 6.0 oz tubes of toothpaste of a particular brand 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 the following data (consistent with what the cited article reported): .53, .65, .46, .50, .37. Does it appear that the true average amount left is less than 10% of the advertised net contents?
a. Check the validity of any assumptions necessary for testing the appropriate hypotheses.
b. Carry out a test of the appropriate hypotheses using a significance level of .05. Would your conclusion change if a significance level of .01 had been used?
c. Describe in context type I and II errors, and say which error might have been made in reaching a conclusion.
Questions & Answers
QUESTION:
Have you ever been frustrated because you could not get a container of some sort to release the last bit of its contents? The article “Shake, Rattle, and Squeeze: How Much Is Left in That Container?” (Consumer Reports, May 2009: 8) reported on an investigation of this issue for various consumer products. Suppose five 6.0 oz tubes of toothpaste of a particular brand 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 the following data (consistent with what the cited article reported): .53, .65, .46, .50, .37. Does it appear that the true average amount left is less than 10% of the advertised net contents?
a. Check the validity of any assumptions necessary for testing the appropriate hypotheses.
b. Carry out a test of the appropriate hypotheses using a significance level of .05. Would your conclusion change if a significance level of .01 had been used?
c. Describe in context type I and II errors, and say which error might have been made in reaching a conclusion.
ANSWER:Step 1 of 4
Given that,
The sample of the remaining toothpaste is 0.53, 0.65, 0.46, 0.50, 0.37.
Sample size=5
Mean,
So,
Standard deviation,
Now, we test theactual average amount of left toothpaste significantly less than 10% of the advertised net content.
Significance level is:
Then, the test statistic is given by,
From the t-table,the critical value of t is -2.13for degrees of freedom 5-1 = 4 at a 0.05 significance level.
Here,
The calculated 
Hence, there is enough evidence to support the claim that the remaining toothpaste is significantly is less than 10% of the advertised net content.